Question

If P = {x : x ∈ N and 1 < x < 11}, Q = {x : x = 2n, n ∈ N and it < 6} and R = {4, 6, 8, 9, 10, 12}, then verify P – (Q ∩ R) = (P – Q) ∪ (P – R).

Answer 1

The roster form of sets P, Q and R are P = {2, 3, 4, 5, 6, 7, 8, 9, 10}, Q = {2, 4, 6, 8, 10} and R = {4, 6, 8, 9, 10, 12} 

First, we find Q ∩ R = {4, 6, 8, 10} 

Then, P – (Q ∩ R) = {2, 3, 5, 7, 9} … (1) 

Next, P – Q = {3, 5, 7, 9} and 

P – R = {2, 3, 5, 7} 

And so, (P – Q) ∪ (P – Q) = {2, 3, 5, 7, 9} ... (2) 

Hence from (1) and (2), it verified that P – (Q ∩ R) = (P – Q) ∪ (P – R) 

Finding the elements of set Q 

Given, x = 2n 

n = 1 → x = 2(1) = 2 

n = 2 → x = 2(2) = 4

n = 3 → x = 2(3) = 6 

n = 4 → x = 2(4) = 8 

n = 5 → x = 2(5) = 10 

Therefore, x takes values such as 2, 4, 6, 8, 10