Question

Find the following sets if ℤ is the universal set: ({x∈ℤ: x ≤ −1}∪{n∈ℤ: n > 4})c

Answer 1

`\{\alpha \in \mathbb{Z} : \alpha > 4 ,\alpha \leq -1\}`

Explanation:

Allowed values for the first set.

`\{x \in \mathbb{Z} : x \leq -1\}`

-1, -2 -3, -4....

Allowed values for the second set.

`\{ n \in \mathbb{Z} : n > 4\}`

5, 6, 7, 8....

Our final set is the union of

`\{-1,-2,-3,-4...\}\cup \{5, 6, 7, 8...\}`

We can represent this as

`\{\alpha \in \mathbb{Z} : \alpha > 4 ,\alpha \leq -1\}`