MATHS [2 Mark Question Answer]

n(A) = 30, n(B) = 27 and n(A ∪ B) = 45
We know that,
n(A-B) = n(A ∪B) – n(B)
n(A – B) = 45 – 27 = 18

n(A) = 45, n(B) = 38 and n(A∪ B) = 70
We know that,
n(B – A) = n(A ∪ B) – n(A)
n(B – A) = 70 – 45 = 25

n(A) = 45, n(B) = 38 and n(A∪ B) = 70
We know that,
n(A-B) = n(A ∪B) - n(B)
n(A – B) = 70 – 38 = 32

n(A) = 45, n(B) = 38 and n(A∪ B) = 70
We know that,
n(A ∩ B) = n(A) + M(B) – n(A ∪B) n(A ∩ B)
= 45 + 38 – 70
= 83 – 70 = 13

n(A) = 75, n(B) = 65 and n(A ∩ B) = 45
We know that,
n(B – A) = n(B) – n(A ∩ B) n(B – A)
= 65 – 45 = 20

n(A) = 75, n(B) = 65 and n(A ∩ B) = 45
We know that,
n(A – B) = n(A) – n(A ∩ B) n(A – B)
= 75 – 45 = 30

n(A) = 75, n(B) = 65 and n(A ∩ B) = 45
We know that,
n( A ∪B) = n(A) + n(B) – n( A ∩ B) n(A ∪B)
= 75 + 65 – 45
n(A∪B) = 140 - 45 = 95

A – B = {2, 4, 6, 8, 10, 12, 14} – {3, 6, 9, 12, 15, 18}
A - B = {2,4, 8, 10, 14}
n(A – B) = 5

A n B = {2, 4, 6, 8, 10, 12, 14} n {3, 6, 9, 12, 15, 18}
A ∩ B = {6,12}
n(A ∩ B) = 2

B = {x: x is a whole number divisible by 3 and x < 18}
B = {3, 6, 9, 12, 15, 18}
n (B) = 6

A = {x : x is natural number divisible-by 2 and x < 16}
A = {2, 4, 6, 8, 10, 12, 14}
n (A) = 7

Natural numbers between 0 and 8 M = {0, 1, 2, 3, 4, 5, 6, 7}
and Natural numbers between 5 to 10 N = {6, 7, 8, 9, 10}
N – M = {8, 9, 10} and n (N – M) = 3

Natural numbers between 0 and 8 M = {0, 1, 2, 3, 4, 5, 6, 7} and
Natural numbers between 5 to 10 N = {6, 7, 8, 9, 10}
M – N = {1, 2, 3, 4} and n (M – N) = 4

Q – P and n (Q – P)
Elements of set P = {1, 2, 3, 4, 6, 12}
Elements of set Q = {1, 2, 4, 8, 16}
∴ Q – P = 8, 16
n (Q - P) = 2

n(A) = 30, n(B) = 27 and n(A ∪ B) = 45
We know that,
n(A ∪B) = n(A) + n(B) – n(A ∪ B)
n(A∪B) = 31 +20 - 6 = 45

n(A) = 30, n(B) = 27 and n(A ∪ B) = 45
We know that,
n(B – A) = n(B) – n(A n B)
n(B – A) = 20 – 6 = 14

n(A) = 31, n(B) = 20 and n(A ∩ B) = 6
We know that,
n(A – B) = n(A) – n(A ∩ B)
n(A - B) = 31 - 6 = 25

C = Set of digits used in 135, = {1,3,5}
∴ Subsets are = { }
or φ, {1}, {3}, {5}, {1,3}, {1,5}, {2,5} and {1, 3, 5}

{x + 3 = 2 and x ∈ N}
x ≠ 3 = 2 ⇒ x = 2 - 3 = -1
which is not a natural number.
∴ It is an empty set.

A = {letters of the word SUPERSTITION}
= {S, U, P, E, R, T, I, O, N}
and B = {letters of the word JURISDICTION}
= (J, U, R, I, S, D, C, T, O, N}
These are neither equal nor equivalent sets as these have different and unequal elements

E = {8, 10, 12, 14, 16}
F = {even natural numbers between 6 and 18}
= {8, 10, 12, 14, 16}
These sets are equal as these have same and equal number of elements.

P = {prime numbers which divide 70 exactly}
= {2, 5, 7}
and Q = {prime numbers which divide 105 exactly}
= {3, 5, 7}
These are equivalent sets as these have equal number of elements.

M = {multiples of 2 and 3 between 10 and 20}
= {12, 14, 15, 16, 18}
and N = {multiples of 2 and 5 between 10 and 20}.
= {12, 14, 15, 16, 18}
These are equal sets as these have same and equal number of elements.

A = {days of the week starting with letter S}
= {Sunday, Saturday}
and B = {days of the week starting with letter T}.
= {Tuesday, Thursday}
These are equivalent sets as both have equal number of elements.

E = {even natural numbers less than 10}
= {2, 4, 6, 8}
and O = {odd natural numbers less than 9}
= {L3, 5, 7}
These are equivalent sets as both have equal number of elements but not the same.

A = Set of letters of the word “FOLLOW”
= {F, O, L, W}
and B = Set of letters of the word “WOLF”.
= = {W, O, L, F}
These are equal sets as these have same and equal. elements.

A = {first four natural numbers}
= {1,2, 3, 4}
and B = {first four whole numbers}
= {0, 1,2,3}
These are equivalent sets as both have equal number of elements but not same.

{people living in Calcutta} and {people living in West Bengal}.
These are not disjoint sets as people of Calcutta are the people of West Bengal as calcutta is a city of West Bengal. So, "people living in West Bengal" is a pair of disjoint sets.

A = {natural numbers less than 10} and B = {x : x is a multiple of 5}
⇒ A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and B = {5, 10, 15 }
These are hot disjoint sets as there is one element 5, which is common.

{0, 1, 2, 6, 8} and {odd numbers less than 10:
⇒ {0, 1,2, 6, 8} and {1,3, 5, 7, 9}
∴ There sets are not disjoint sets as there is one element (1) is common.

K = {x : x is an integer and – 3 < x < 5}:
∵ – 3 < x < 5
∴ x lies between – 3 and 5
∴ K = {- 2, – 1, 0, 1, 2, 3, 4}