If P = {letters of the word HYDERABAD} and Q = {letters of the word ALLAHABAD}, find P ∪ Q P ∩ Q Also verify that n P ∪ Q = n P + n Q - n P ∩ Q .

Given that P = {letters of the word HYDERABAD} P = H , Y , D , R , E , A , B ⇒ n P = 7 and Q = {letters of the word ALLAHABAD}, Q = A , L , B , H , D ⇒ n Q = 5 Let us find union and intersection of two sets. P ∪ Q = H , Y , D , R , L , E , A , R ⇒ n P ∪ Q = 8 P ∩ Q = A , H , B , D ⇒ n P ∩ Q = 4 To verify the given condition n P ∪ Q = n P + n Q - n P ∩ Q L H S = n P ∪ Q = 8 . . . 1 R H S = n P + n Q - n P ∩ Q = 7 + 5 - 4 = 12 - 4 = 8 Therefore, L H S = R H S . Hence, the given condition is verified.

If P = {letters of the word HYDERABAD} and Q = {letters of the word ALLAHABAD}, find P ∪ Q P ∩ Q Also verify that n P ∪ Q = n P + n Q - n P ∩ Q .

Given that P = {letters of the word HYDERABAD} P = H , Y , D , R , E , A , B ⇒ n P = 7 and Q = {letters of the word ALLAHABAD}, Q = A , L , B , H , D ⇒ n Q = 5 Let us find union and intersection of two sets. P ∪ Q = H , Y , D , R , L , E , A , R ⇒ n P ∪ Q = 8 P ∩ Q = A , H , B , D ⇒ n P ∩ Q = 4 To verify the given condition n P ∪ Q = n P + n Q - n P ∩ Q L H S = n P ∪ Q = 8 . . . 1 R H S = n P + n Q - n P ∩ Q = 7 + 5 - 4 = 12 - 4 = 8 Therefore, L H S = R H S . Hence, the given condition is verified.