Q. The roster form of a set T = {x: x is an integers greater than -2 and less than 4) is

To express the set T in roster form, we need to identify all the integers that satisfy the condition given in the set description: "x is an integer greater than -2 and less than 4."

Break Down the Problem

1. Identify the integers greater than -2.
2. Identify the integers less than 4.
3. Combine the two conditions to form the set.

Relevant Concepts

• The integers greater than -2 are those that are -1, 0, 1, 2, 3, etc.
• The integers less than 4 are 3, 2, 1, 0, -1, etc.
• We need to find the overlap of these two sets based on the given conditions.

Analysis and Detail

The integers greater than -2 are:

• -1, 0, 1, 2, 3

The integers less than 4 are:

• 3, 2, 1, 0, -1

Now, we combine both conditions. The set T will include all integers that are both greater than -2 and less than 4.

The resulting set T in roster form is:

• $T = \{-1, 0, 1, 2, 3\}$

Verify and Summarize

We've carefully analyzed the integers based on the conditions, and the final roster form of set T has been verified.

Final Answer

The roster form of the set $T$ is $T = \{-1, 0, 1, 2, 3\}$.