Question 11 Mark
Given, $A = \{$Quadrilaterals$\}, B = \{$Rectangles$\}, C = \{$Squares$\}, D= \{$Rhombuses$\}.$ State the following statement is true or false. Give reasons. $ A ⊇ B ⊇ D$
AnswerFalse.
Explanation:
$A = \{$Quadrilaterals$\}$
$B = \{$Rectangles$\}$
$C = \{$Squares$\}$
$D= \{$Rhombuses$\}$
$A ⊇ B ⊇ D .....$False
$\because$ Rhombus is not a rectangle also.
View full question & answer→Question 21 Mark
Given, $A = \{$Quadrilaterals$\}, B = \{$Rectangles$\}, C = \{$Squares$\}, D= \{$Rhombuses$\}$. State the following statement is true or false. Give reasons. $B ⊇ C$
AnswerTrue.
Explanation:
$A = \{$Quadrilaterals$\}$
$B = \{$Rectangles$\}$
$C = \{$Squares$\}$
$D = \{$Rhombuses$\}$
$B ⊇ C ....$True
$\because$ Square is a rectangle also.
View full question & answer→Question 31 Mark
Given, $A = \{$Quadrilaterals$\}, B = \{$Rectangles$\}, C = \{$Squares$\}, D= \{$Rhombuses$\}$. State the following statement is true or false. Give reasons. $D ⊂ A$
AnswerTrue
Explanation:
Given, $A = \{$Quadrilaterals$\}$
$B = \{$Rectangles$\}$
$C = \{$Squares$\}$
$D= \{$Rhombuses$\}$
$D ⊂ A ....$.True
$\because $ Rhombus is one of the quadrilaterals.
View full question & answer→Question 41 Mark
Given, $A = \{$Quadrilaterals$\}, B = \{$Rectangles$\}, C = \{$Squares$\}, D= \{$Rhombuses$\}$. State the following statement is true or false. Give reasons. $C ⊆ B ⊆ A$
AnswerTrue
Explanation:
$A = \{$Quadrilaterals$\}$
$B = \{$Rectangles$\}$
$C = \{$Squares$\}$
$D= \{$Rhombuses$\}$
$C ⊆ B ⊆ A ....$True
$\because$ Every square is a rectangle also and every rectangle is a quadrilateral also.
View full question & answer→Question 51 Mark
Given, $A = \{$Quadrilaterals$\}, B = \{$Rectangles$\}, C = \{$Squares$\}, D= \{$Rhombuses$\}$. State the following statement is true or false. Give reasons. $D ⊂ B$
AnswerFalse
Explanation:
$A = \{$Quadrilaterals$\}$
$B = \{$Rectangles$\}$
$C = \{$Squares$\}$
$D= \{$Rhombuses$\}$
$D ⊂ B ..... $is a False.
$\because$ Rhombus is not a rectangle also.
View full question & answer→Question 61 Mark
Given, $A = \{$Quadrilaterals$\}, B = \{$Rectangles$\}, C = \{$Squares$\}, D= \{$Rhombuses$\}$.State the following statement is true or false. Give reasons. $B ⊂ C$
AnswerFalse.
Explanation:
$A = \{$Quadrilaterals$\}$
$B = \{$Rectangles$\}$
$C = \{$Squares$\}$
$D= \{$Rhombuses$\}$
$B ⊂ C .....$is a False.
$\because$ Rectangle is not a square also.
View full question & answer→Question 71 Mark
Given, $A = \{$Triangles$\}, B = \{$Isosceles triangles$\}, C = \{$Equilateral triangles$\}$. State the following statement is true or false. Give reasons. $C ⊆ B ⊆ A $
AnswerTrue.
Explanation:
$A = \{$Triangles$\}$
$B = \{$Isosceles triangles$\}$
$C = \{$Equilateral triangles$\}$
$C ⊆ B ⊆ A ....$True
$\because$ Each equilateral triangle is isosceles also and each isosceles $\triangle$ is a form of triangles.
View full question & answer→Question 81 Mark
Given, $A = \{$Triangles$\}, B = \{$Isosceles triangles$\}, C = \{$Equilateral triangles$\}$. State the following statement is true or false. Give reasons. $C ⊂ A $
AnswerTrue.
Explanation:
$A = \{$Triangles$\}$
$B = \{$Isosceles triangles$\}$
$C = \{$Equilateral triangles$\}$
$C ⊂ A ....$True
$\because$ Equilateral \triangle is one of the triangles.
View full question & answer→Question 91 Mark
Given, $A = \{$Triangles$\} B = \{$Isosceles triangles$\} C = \{$Equilateral triangles$\}$. State the following statment is true or false. Give reasons. $B ⊂ A$
AnswerTrue.
Explanation:
$A = \{$Triangle$\}$
$B = \{$Isosceles triangles$\}$
$C = \{$Equilateral triangles$\}$
$B ⊂ A ....$True
$\because$ Isosceles $\triangle$ is one of the triangles.
View full question & answer→Question 101 Mark
Given, $A = \{$Triangles$\}, B = \{$Isosceles triangles$\}, C = \{$Equilateral triangles$\}$. State the following statement is true or false. Give reasons. $C ⊆ B$
AnswerTrue.
Explanation:
$A = \{$Triangles$\}$
$B = \{$Isosceles triangles$\}$
$C = \{$Equilateral triangle$\}$
Since each equilateral triangle is isosceles also,
$\therefore C ⊆ B ....$True
View full question & answer→Question 111 Mark
Given, $A = \{$Triangles$\}, B = \{$Isosceles triangles$\}, C = \{$Equilateral triangles$\}$. State the following statement is true or false. Give reasons. $B ⊆ A$
AnswerTrue
Explanation:
$A = \{$Triangles$\}$
$B = \{$Isosceles triangles$\}$
$C = \{$Equilateral triangle$\}$
$B ⊆ A ... $True
$\because$ Isosceles $\triangle$ is one of the triangles.
View full question & answer→Question 121 Mark
Given, $A = \{$Triangles$\}, B = \{$Isosceles triangles$\}, C = \{$Equilateral triangles$\}$. State the following statement is true or false. Give reasons.$A ⊂ B$
AnswerFalse.
Reason:
$A = \{$Triangles$\}$
$B = \{$Isosceles triangles$\}$
$C = \{$Eqilateral triangles$\}$
Since each triangle is not isosceles.
$\therefore A ⊂ B$
Hence,$ A ⊂ B$ is false.
View full question & answer→Question 131 Mark
State the following statement is true or false : $n(A) = n(B) => A = B.$
AnswerFalse
Explanation:
$n(A) = n(B)$
$\Rightarrow$ Number of elements of set $A$
$=$ Number of elements of set $B$
$\therefore$ Given sets are equivalent but not equal.
$\therefore "n(A) = n(B) \Rightarrow A = B" ..........$is a False statement.
View full question & answer→Question 141 Mark
State the following statement is true or false : If set $P =$ set $M$, then $n(P) = n(M).$
AnswerTrue.
Explanation:
Set $P =$ Set $M$
It means sets $P$ and M are equal. Equal sets are equivalent also.
$\therefore$ Number of elements of set $P =$ Number of elements of set $M$
$\therefore$ "If set $P =$ set $M$, then $n(P) = n(M)" ........$is a True statement.
View full question & answer→Question 151 Mark
State the following statement is true or false: In $n(P) = n(M)$, then $P → M.$
AnswerTrue
Explanation:
$n(P) = n(M)$
It means number of elements of set $P$
$=$ Number of elements of set $M.$
$\therefore$ Sets $P$ and $M$ are equivalent.
$\therefore$ "If $n(P) = n(M)$, then $P \leftrightarrow M" ... $is a True statement.
View full question & answer→Question 161 Mark
State the following statement is true or false : The set of squares of integers and the set of whole numbers are equal sets.
AnswerFalse.
Explanation:
Integer Square of Integer Whole No.
$0$ : $(0)^2 = 0$ $ 0$
$±1$ : $(±1)^2 = 1$ $1$
$±2$ : $(±2)^2 = 4$ $2$
$±3$ : $(±3)^2= 9$ $3$
$±4$ : $(±4)^2 = 16$ $4$
$±5$ : $(±5)^2 = 25$ $5$
$..... : ..... ..... .....$
$..... : ..... ..... .....$
$\therefore$ Set of square of integers
$= {0, 1, 4, 9, 16, 25,.......}$
Set of whole numbers$ = {0, 1, 2, 3, 4, 5, 6, 7,....}$
Hence "The set of square of integers and the set of whole numbers are equal$...$False statement.
View full question & answer→Question 171 Mark
State the following statement is true or false : The set of odd prime numbers is the empty set.
AnswerFalse.
Explanation:
Set of odd prime numbers
$= \{3, 5, 7, 11, 13, 17, 19, 23,....\}$
$\therefore$ "The set of odd prime numbers is the empty set" $......$is a False statement.
View full question & answer→Question 181 Mark
State the following statement is true or false : If $A = \{x : x$ is an even prime number$\}$, then set $A$ is empty.
AnswerFalse.
Explanation:
$A = \{x : x$ is an even prime number$\} = {2}$
$\therefore$ "If $A = \{x : x$ is an even Prime number$\}$, then set $A$ is empty" $.....$ is a False statement.
View full question & answer→Question 191 Mark
State the following statement is true or false : The set $A = \{$integers less than $20\}$ is a finite set.
AnswerFalse.
Explanation:
$A = \{$Integers less than $20\}$
$= \{19, 18, 17, 16,.....,0, -1, -2, -3,....\}$
$\therefore$ "The set $A = \{$Integers less than $20\}$ is a finite set"$......$is a False statement.
View full question & answer→Question 201 Mark
State the following statement is true or false: If $E = \{$factors of $16\}$ and $F = \{$factors of $20\}$, then $E = F.$
AnswerFalse.
E\timesplanation:
$E = \{$Factors of $16\}$
$= \{1, 2, 4, 8, 16\}$
$1 \times 16 = 16$
$2 \times 8 = 16$
$4 \times 4 = 16$
$F = \{$Factors of $20\}$
$= \{1, 2, 4, 5, 10, 20\}$
$1 \times 20 = 20$
$2 \times 10 = 20$
$4 \times 5 = 20$
Now we see that elements of set $E$ and set $F$ are not the same $($identical$)$
$\therefore$ "if $E = \{$Factors of $16\}$ and $F = \{$Factors of $20\}$, then $E = F"......$is a False statement.
View full question & answer→Question 211 Mark
State the following statement is true or false: The set of even natural numbers less than $21$ and the set of odd natural numbers less than $21$ are equivalent sets.
AnswerTrue.
Explanation:
Set of even natural number less than $21$
$= \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}$
$\therefore$ Cardinal Number of this set $= 10$
Set of odd natural numbers less than $21$
$= \{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\}$
$\therefore$ Cardinal number of this set $= 10$
Now we see that cardinal number of both these sets $= 10$
$\therefore$ "The set of even natural numbers less than $21$ and the set of odd natural numbers less than $21$ are equivalent sets". Hence it is a True statement.
View full question & answer→