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)

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}