Categories:
ICSE

Question 1.

If A = {0, 1, 2, 3, …….., 8}, B = {3, 5, 7, 9, 11} and C = {0, 5, 10, 20}, find

(i) A ∪ B

(ii) A ∪ C

(iii) B ∪ C

(iv) A ∩ B

(v) A ∩ C

(vi) B ∩ C

Also find the cardinal number of the sets B ∪ C, A ∪ B, A ∩ C and B ∩ C.

Solution:

Question 2.

Find A’ when

(i) A= {0, 1, 4, 7} and E, = {x | x ϵ W, x ≤ 10}

(ii) A = {consonants} and ξ = {alphabets of English}

(iii) A = boys in class VIII of all schools in Bengaluru} and ξ = {students in class VIII of all schools in Bengaluru}

(iv) A = {letters of KALKA} and ξ = {letters of KOLKATA}

(v) A = {odd natural numbers} and ξ = {whole numbers}.

Solution:

Question 3.

If A {x : x ϵ N and 3 < x < 1} and B = {x : x ϵ Wand x ≤ 4}, find

(i) A ∪ B

(ii) A ∩ B

(iii) A – B

(iv) B – A

Solution:

Question 4.

If P = {x : x ϵ W and x < 6} and Q = {x : x ϵ N and 4 ≤ x ≤ 9}, find

(i) P ∪ Q

(ii) P ∩ Q

(iii) P – Q

(iv) Q – P

Is P ∪ Q a proper superset of P ∩ Q ?

Solution:

Question 5.

If A = (letters of word INTEGRITY) and B = (letters of word RECKONING), find

(i) A ∪ B

(ii) A ∩ B

(iii) A – B

(iv) B – A

Also verify that:

(a) n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

(b) n(A – B) = n(A ∪ B) – n(B)

= n(A) – n(A ∪ B)

(c) n(B – A) = n(A ∪ B) – n(A)

= n(B) – n(A ∩ B)

(d) n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).

Solution:

Question 6.

If ξ = {natural numbers between 10 and 40}

A = {multiples of 5} and

B = {multiples of 6}, then

(i) find A ∪ B and A ∩ B

(ii) verify that

n(A ∪ B) = B (A) + n(B) – n(A ∩ B).

Solution:

Question 7.

If ξ ={1,2, 3, …. 9}, A = {1, 2, 3, 4, 6, 7, 8} and B = {4, 6, 8}, then find.

(i) A’

(ii) B’

(iii) A ∪ B

(iv) A ∩ B

(v) A – B

(vi) B – A

(vii) (A ∩ B)’

(viii) A’ ∪ B’

Also verify that:

(a) (A ∩ B)’ = A’ ∪ B’

(b) n(A) + n(A’) = n(ξ)

(c) n(A ∩ B) + n((A ∩ B)’) = n(ξ)

(d) n(A – B) + n(B – A) + n(A ∩ B)

= n(A ∪ B).

Solution:

Question 8.

If 4 = {x : x ϵ W, x ≤ 10}, A. = {x : x ≥ 5} and B = {x : 3 ≤ x < 8}, then verify that:

(i) (A ∪ B)’ = A’ ∩ B’

(ii) (A ∩ B)’= A’ ∪ B’

(iii) A – B = A ∩ B’

(iv) B – A = B ∩ A’

Solution:

Question 9.

If n(A) = 20, n(B) = 16 and n(A ∪ B) = 30, find n(A ∩ B).

Solution:

Question 10.

If n ξ = 20 and n(A’) = 7, then find n(A).

Solution:

Question 11.

If n(ξ) = 40, n(A) = 20, n(B’) = 16 and n(A ∪ B) = 32, then find n(B) and n(A ∩ B).

Solution:

Question 12.

If n(ξ) = 32, n(A) = 20, n(B) = 16 and n((A ∪ B)’) = 4, find :

(i) n(A ∪ B)

(ii) n(A ∩ B)

(iii) n(A – B)

Solution:

Question 13.

If n(ξ) = 40, n(A’) = 15, n(B) = 12 and n((A ∩ B)’) = 32, find :

(i) n(A)

(ii) n(B’)

(iii) n(A ∩ B)

(iv) n(A ∪ B)

(v) n(A – B)

(vi) n(B – A)

Solution:

Question 14.

If n(A – B) = 12, n(B – A) = 16 and n(A ∩ B) = 5, find:

(i) n(A)

(ii) n(B)

(iii) n(A ∪ B)

Solution:

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