Question

Write each of the following sets by listing their elements between braces. $$ \\{x \in \mathbb{Z}:-2 \leq x<7\\} $$

Short answer

\{-2, -1, 0, 1, 2, 3, 4, 5, 6\}

Step-by-step solution

Identify the lower and upper bounds of the set

The given set includes all elements \(x\) from the integer set \(\mathbb{Z}\) such that \(-2 \leq x < 7\). Therefore, the lower bound of this set is -2, and the upper bound is 7. However, the upper bound 7 is not included in the set because the inequality is '<' and not '\leq'.

List the elements within the bounds

Starting from the lower bound (-2), list all integers up to, but not including, the upper bound (7). Organise the numbers in ascending order, since this is common practice but technically not necessary.

Write down the set by listing its elements

Now that all the elements have been identified, write down the set by enclosing the elements in braces.