Solution to Set Operations

Example 2.2.1:

List the members of the set

i. { y : 1 < y ≤ 6, y ϵ N}
ii. { y : y > -5, y ϵ Z^+}
iii. {y : y > 8, y ϵ Z^–}
iv. {y : 3 < y < 8, y ϵ N}
v. {y : y is a prime factor of 30 and 42}

Solution

i. { y : 1 < y ≤ 6, y ϵ N}

This means that y is greater than 1 and less than or equal to 6.

Therefore,

{2, 3, 4, 5, 6}

(Note that element 1 is not included, however, element 6 is included i.e. when the inequality sign comes with an equality sign the element is included and if otherwise it is not included).

ii. { y : y > -5, y ϵ Z^+}

(1, 2, 3, 4, 5, …} y is positive numbers greater than -5

(Note that zero is an integer, however, it is not included because zero is neither positive nor negative. Also -4… -1 are not included because they are not members of Z⁺.