Question 3 :

Let P = {a, b, c}, Q = {g, h, x, y} and R = {a, e, f, s}. Find the following

(i) P \ R (ii) Q ∩ R (iii) R \ (P ∩ Q)

Solution :

(i) To find P \ R we have to choose the common elements from both P and R and we have to write remaining elements in P.

P \ R = {a, b, c} \ {a, e, f, s}

= {b, c}

(ii) To find Q ∩ R we have to write the common elements in Q and R.

Q ∩ R = {g,h,x,y} ∩ {a,e,f,s}

there is no common elements in both Q and R

Q ∩ R = Ø

(iii) R \ (P ∩ Q)

P ∩ Q = {a,b,c} ∩ {g,h,x,y}

There is no common elements in both P and Q

P ∩ Q = Ø

R \ (P ∩ Q) = {a,b,c} \ Ø

= {a,b,c}