(Each question 1 marks)

Question 511 Mark

If U = {a, b, c, d, e, f, g, h}, find the complement of the set: D = {f, g, h, a}

Answer

$D' = U - D = \{ a,b,c,d,e,f,g,h\} - \{ f,g,h,a\}$={b, c, d, e}

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Question 521 Mark

If U = {a, b, c, d, e, f, g, h}, find the complement of the set: C = {a, c, e, g}

Answer

$C' = U - C = \{ a,b,c,d,e,f,g,h\} - \{ a,c,e,g\}$= {b, d, f, h}

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Question 531 Mark

If U = {a, b, c, d, e, f, g, h}, find the complement of the set: B = {d, e, f, g}

Answer

$B' = U - B = \{ a,b,c,d,e,f,g,h\} - \{ d,e,f,g\}$={a, b, c, h}

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Question 541 Mark

If U = {a, b, c, d, e, f, g, h}, find the complement of the set: A = {a, b, c}

Answer

$A' = U - A = \{ a,b,c,d,e,f,g,h\} - \{ a,b,c\}$= {d, e, f, g, h}

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Question 551 Mark

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find:(B - C)'

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
B - C = {2, 4, 6, 8} - {3, 4, 5, 6}
= {2, 8}
(B - C)' = U - (B - C) = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 8}
= {1, 3, 4, 5, 6, 7, 9}

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Question 561 Mark

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find:(A')'

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A' = U - A' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {5, 6, 7, 8, 9}
= {5, 6, 7, 8, 9}
A' = U - A' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {5, 6, 7, 8, 9}
= {1, 2, 3, 4} = A

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Question 571 Mark

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find: $(A \cup B)'$

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
$A \cup B $ = {1, 2, 3, 4} $ \cup $ {2, 4, 6 ,8}
= {1, 2, 3, 4, 6, 8}
$(A \cup B)' = U - (A \cup B)$ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 6, 8}
= {5, 7, 9}

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Question 581 Mark

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}.
Find: $(A \cup C)'$

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
$A \cup C$= {1, 2, 3, 4} $ \cap ${3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6}
$(A \cup C)' = U - (A \cup C)$= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 5, 6}
={7, 8, 9}

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Question 591 Mark

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find: B'

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}
B' = U - B= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}
= {1, 3, 5, 7, 9}

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Question 601 Mark

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find :$\begin{equation} \mathbf{A}^{\prime} \end{equation}$

Answer

wehave to find the complement of,which is given by (U - A)
WhereU = {1, 2, 3, 4, 5, 6, 7, 8, 9} andA = {1, 2, 3, 4},
$\therefore$$\begin{equation} \mathbf{A}^{\prime} \end{equation}$= U - A
$\Rightarrow$ $\begin{equation} \mathbf{A}^{\prime} \end{equation}$= {1, 2, 3, 4, 5, 6, 7, 8, 9} -{1, 2, 3, 4}
$\Rightarrow$ $\begin{equation} \mathbf{A}^{\prime} \end{equation}$={5, 6, 7, 8, 9}

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Question 611 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find:C - B

Answer

Here A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}

C - B = {2,4,6,8,10,12,14,16} - {4,8,12,16,20}
= {2,6,10,14}

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Question 621 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}. Find: B - D.

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
B - D = {4, 8, 12, 16, 20} - {5, 10, 15, 20}
= {4, 8, 12, 16}

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Question 631 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}. Find:B - C

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
B - C = {4, 8, 12, 16, 20} - {2, 4, 6, 8, 10, 12, 14, 16}
= {20}

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Question 641 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}. Find:D - A

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
D - A = {5, 10, 15, 20} - {3, 6, 9, 12, 15, 18, 21}
= {5, 10, 20}

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Question 651 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find:C - A

Answer

Here A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}

C - A = {2,4,6,8,10,12,14,16} - {3,6,9,12,15,18,21}
= {2,4,8,10,14,16}

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Question 661 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: B - A

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
B - A = {4, 8, 12, 16, 20} - {3, 6, 9, 12, 15, 18, 21}
= {4, 8, 16, 20}

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Question 671 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find:A - D

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
A - D = {3, 6, 9, 12, 15, 18, 21} - {5, 10, 15, 20}
= {3, 6, 9, 12, 18, 21}

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Question 681 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: A - C

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
A - C = {3, 6, 9, 12, 15, 18, 21} - {2, 4, 6, 8, 10, 12, 14, 16}
={3, 9, 15, 18, 21}

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Question 691 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find:D - C

Answer

Here A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
D - C = {5,10,15,20} - {2,4,6,8,10,12,14,16}
= {5,15,20}

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Question 701 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find:C - D

Answer

Here A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}

C - D = {2,4,6,8,10,12,14,16} - {5,10,15,20}
= {2,4,6,8,12,14,16}

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Question 711 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find:D - B

Answer

Here A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}

D - B = {5,10,15,20} - {4,8,12,16,20}
= {5,10,15}

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Question 721 Mark

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: A - B

Answer

Here A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
A - B = {3, 6, 9, 12, 15, 18, 21} - {4, 8, 12, 16, 20}
= { 3, 6, 9, 15, 18, 21}

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Question 731 Mark

Given pairof sets are disjoint?{x : x is an even integer} and {x : x is an odd integer}

Answer

Let A = {x : x is an even integer}
and B = {x : x is an odd integer}
$\therefore A \cap B = \phi $
Hence A and B are disjoint.

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Question 741 Mark

Given pairof sets are disjoint?{a, e, i, o, u} and {c, d, e, f}

Answer

(ii) Let A = {a, e, i, o, u}
and B = {c, d, e, f}
$\therefore A \cap B ≠ \phi$
Hence A and B are not disjoint.

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Question 751 Mark

Given pairof sets are disjoint?{1, 2, 3, 4} and {x : x is a natural number and$4 \leq x \leq 6$

Answer

Let A = {1, 2, 3, 4}
and B = {x : x is a natural number and $4 \leq x \leq 6$
= {4, 5, 6}
$\therefore A \cap B = \{ 1,2,3,4\} \cap \{ 4,5,6\}$
= {4}
Hence A and B are not disjoint.

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Question 761 Mark

If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find:$C \cap D$

Answer

Here A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . }

$C \cap D$= {x : x is an odd natural number} $ \cap ${x : x is a prime number}
= {x : x is an odd prime number}

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Question 771 Mark

If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find:$B \cap D$

Answer

$B \cap D$= {x : x is an even natural number) $ \cap ${x : x is a prime number}
= {2}

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Question 781 Mark

If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find:$B \cap C$

Answer

$B \cap C$= {x : x is an even natural number} $ \cap${x : x is an odd natural number}
$ = \phi $

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Question 791 Mark

If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find:$A \cap D$

Answer

$A \cap D$= {x : x is a natural number) $ \cap${x : x is a prime number}
= {x : x is a prime number}
= D

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Question 801 Mark

If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $A \cap C$

Answer

$A \cap C$= {x : x is a natural number} $ \cap ${x : x is an odd natural number}
= { x : x is an odd natural number }
= C

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Question 811 Mark

If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $A \cap B$?

Answer

$A \cap B$= {x :x is a natural number)$ \cap ${x : x is an even natural number}
= {x : x is an even natural number}
= B

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Question 821 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:$(A \cap B) \cap (B \cup C)$

Answer

Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

$(A \cap B) \cap (B \cup C) =$$(\{ 3,5,7,9,11\} \cap \{ 7,9,11,13\} ) \cap (\{ 7,9,11,13\} \cup \{ 11,13,15\} )$
$ = \{ 7,9,11\} \cap \{ 7,9,11,13,15\}$
= {7, 9, 11}

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Question 831 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:$A \cap (B \cup D)$

Answer

Here A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17}

$A \cap (B \cup D) = $$A \cap (B \cup D) = \{ 3,5,7,9,11\} \cap (\{ 7,9,11,13\} \cup \{ 15,17\} )$
$ = \{ 3,5,7,9,11\} \cap \{ 7,9,11,13,15,17\} $
= {7,9, 11}

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Question 841 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find$A \cap D$

Answer

Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

$A \cap D = \{ 3,5,7,9,11\} \cap \{ 15,17\} = \phi $

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Question 851 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:$A \cap (B \cup C)$

Answer

Here A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17}

$A \cap (B \cup D) = \{ 3,5,7,9,11\} \cap (\{ 7,9,11,13\} \cup \{ 11,13,15\} )$
$ = \{ 3,5,7,9,11\} \cap \{ 7,9,11,13,15\} $
= {7, 9, 11}

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Question 861 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:$B \cap D$

Answer

Here A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17}

$B \cap D = \{ 7,9,11,13\} \cap \{ 15,17\} = \phi $

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Question 871 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find$A \cap C$

Answer

Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

$A \cap C = \{ 3,5,7,9,11\} \cap \{ 11,13,15\}$= {11}

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Question 881 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find$A \cap C \cap D$

Answer

Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

$A \cap C \cap D = \{ 3,5,7,9,11\} \cap \{ 11,13,15\} \cap \{ 15,17\} = \phi $

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Question 891 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find$B \cap C$

Answer

Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

$B \cap C = \{ 7,9,11,13\} \cap \{ 11,13,15\} $= {11, 13}

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Question 901 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:$(A \cup D) \cap (B \cup C)$

Answer

Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

$(A \cup D) \cap (B \cup C) = $$(\{ 3,5,7,9,11\} \cup \{ 15,17\} ) \cap (\{ 7,9,11,13\} \cup \{ 11,13,15\} )$
$ = \{ 3,5,7,9,11,13,15,17\} \cap \{ 7,9,11,13,15\}$
= {7, 9, 11,15}

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Question 911 Mark

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $A \cap B$?

Answer

Here A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17}

$A \cap B = \{ 3,5,6,7,11\} \cap \{ 7,9,11,13\} = \{ 7,9,11\}$

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Question 921 Mark

Find the intersectionpair ofthe set :A = {1, 2, 3}, B =$\phi$

Answer

We have,
A = {1, 2, 3}
And, B =$\phi$
$\therefore$A$\cap$B ={$\phi$}

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Question 931 Mark

Find the intersectionpair ofthe set :A = {x : x is a natural number and 1 < x $\leq$6 }, B = {x : x is a natural number and 6 < x < 10}

Answer

We have,
A = {2, 3, 4, 5, 6}
And, B = {7, 8, 9}
$\therefore$A$\cap$B = {$\phi$}

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Question 941 Mark

Find the intersectionpair ofthe set :A = {x : x is a natural number and multiple of 3}, B = {x : x is a natural number less than 6}

Answer

Given,
A = {3, 6, 9, 12, 15, 18, ....}
And, B = {1, 2, 3, 4, 5}
$\therefore$A$\cap$B = {a}

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Question 951 Mark

Find the intersectionpair ofthe set :A = {a, e, i, o, u} B = {a, b, c}

Answer

We have
A = {a, e, i, o, u}
And, B = {a, b, c}
$\therefore$A$\cap$ B = {a}

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Question 961 Mark

Find the intersectionpair ofthe set :X = {1, 3, 5} Y = {1, 2, 3}

Answer

Here, we have
X = {1, 3, 5}
And, Y = {1, 2, 3}
$\therefore$X$\cap$ Y = {1, 3}

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Question 971 Mark

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find:$B \cup C \cup D$

Answer

Here A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10}

$B \cup C \cup D =$
$= \{ 3,4,5,6\} \cup \{ 5,6,7,8\} \cup \{ 7,8,9,10\}$
$= \{ 3,4,5,6,7,8\} \cup \{ 7,8,9,10\}$
= {3, 4, 5, 6, 7, 8, 9,10}

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Question 981 Mark

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find:$A \cup B \cup D$

Answer

Here A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10}

$A \cup B \cup D = \{ 1,2,3,4\} \cup \{ 3,4,5,6\} \cup \{ 7,8,9,10\}$
$= \{ 1,2,3,4,5,6\} \cup \{ 5,6,7,8\}$
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

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Question 991 Mark

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find:$A \cup B \cup C$

Answer

Here A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10}

$A \cup B \cup C = \{ 1,2,3,4\} \cup \{ 3,4,5,6\} \cup \{ 5,6,7,8\} $
$= \{ 1,2,3,4,5,6\} \cup \{ 5,6,7,8\}$
= {1, 2, 3,4, 5, 6, 7, 8}

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Question 1001 Mark

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find:$B \cup D$

Answer

Here A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10}

$B \cup D = \{ 3,4,5,6\} \cup \{ 7,8,9,10\}$= {3, 4, 5, 6, 7, 8, 9, 10}

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MATHS (Each question 1 marks)