Q. Which is the set of integers greater than −4 and less than or equal to 1?Choices:(A) {0,1}(B) {−3,−2,−1,0,1}(C) {−4,0,1}(D) {−4,−3,−2,−1,0,1}
Identify Inequality Condition: Identify the inequality that represents the condition "greater than −4 and less than or equal to 1".The inequality for this condition is -4 < x \leq 1, where x is an integer.
Determine Satisfying Integers: Determine the set of integers that satisfy the inequality -4 < x \leq 1. The integers greater than −4 are −3,−2,−1,0,1,2,3,… However, we also need to consider that x must be less than or equal to 1. Therefore, we exclude any integers greater than 1.
List Satisfying Integers: List the integers that satisfy both conditions.The integers that are greater than −4 and less than or equal to 1 are: −3, −2, −1, 0, 1.
Match with Choices: Match the set of integers from Step 3 with the given choices.The correct set of integers is (B){−3,−2,−1,0,1}.