Question

Set Let U= {x: 10 ≤ x ≤ 20, xe N} be a universal set. P and Q are the subsets of U suc that P ={y: y is an even number) and Q = {z: z is a multiple of 3)

(a) List the elements of P - Q.

Answer 1

The elements of P−Q are y: y is an even number and is not a multiple of 3

The set P−Q represents the elements that are in set P (even numbers) but not in set Q (multiples of 3) within the universal set U, where U consists of natural numbers between 10 and 20 (inclusive). To find P−Q, we identify the elements that meet the criteria of being even numbers but not multiples of 3.

Considering the even numbers between 10 and 20, we observe that the elements 10, 12, 14, 16, 18, and 20 are in set P. Eliminating the multiples of 3 from this list, we exclude 12 and 18. Therefore, the elements of P−Q are 10, 14, 16, and 20, representing even numbers that are not multiples of 3 within the specified range.