Question

Let A and B be two overlapping sets and the universal set be U. Draw appropriate Venn
diagram for each of the following,
(i) A∪B (ii) A∩B (iii) (A∩B)′ (iv) (B–A)′ (v) A′∪B′ (vi) A′∩B′
(vii) What do you observe from the Venn diagram (iii) and (v)?

Answer 1

Solution:-

given by sets:-
(i) A∪B (ii) A∩B (iii) (A∩B)′ (iv) (B–A)′ (v) A′∪B′ (vi) A′∩B′

Acourding two question :-

let = U = { 1 ,2,3,4,5,6,7,}

》 A = { 1,2,3,4,} B = {4,6,7,8,9}

(i) A∪B

》ans:- A∪B = { 1 ,2,3,4,5,6,7}

(ii) A∩B

》ans:- A∩B = {4}


(iii)(A∩B)′

》ans:- A∩B = {4} , U = {{ 1 ,2,3,4,5,6,7,}

》(A∩B)′ = {1,2,3,5,6,7}

》(iv)(B–A)′

》ans :- B - A = {5,6,7,} U = {{ 1 ,2,3,4,5,6,7,}

》(B–A)′ = { 1,2,3,4}

(v) A′∪B′

》ans:- here A' = {5,6,7} B' = {1,2,3,4}

》A′∪B′ = {1,2,3,4,5,6,7}

(vi)A′∩B′

》ans:- A' = {5,6,7} B' = {1,2,3,4}

》A′∪B′ = { }

☆i hope its help☆