Q. 5

Let A = {2, 3, 5, 7, 11, 13}, B = {5, 7, 9, 11, 15} be subsets of U = {2, 3, 5, 7, 9, 11, 13, 15}.

Using Venn diagrams, verify that:

(i) (A B’) = (A’ B’)

(ii) (A B)’ = (A’ B’)

Answer :



(i) Here blue region denotes set A - B


The green region denotes set B - A


The overlapping region denotes AB, and the orange region denotes the universal set U.


From the Venn diagram we get (AB’) = {2, 3, 5, 7, 11, 13} (B’ is the set excluding those elements present in set B i.e. A - B region)


A’ = {9, 15} and B’ = {2, 3, 13}


Therefore A’B’ = {}


Therefore (A B’) (A’ B’) [Verified]


(ii) From the Venn diagram we get (A B)’ = {2, 3, 9, 13, 15} (elements except those present in A B)


(A’ B’) = {2, 3, 9, 13, 15}


Therefore, (A B)’ = (A’ B’) [Verified]


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