Q. Which is the set of integers greater than or equal to 2 and less than 6?Choices:(A) {3,4,5,6}(B) {3,4,5}(C) {2,3,4,5}(D) {2,6}
Identify Inequalities: Identify the inequality that represents the set of integers greater than or equal to 2 and less than 6.We are looking for two inequalities here: one that represents "greater than or equal to 2" and another that represents "less than 6".The inequality for "greater than or equal to 2" is x≥2.The inequality for "less than 6" is x < 6 .
Combine Inequalities: Combine the inequalities to form a compound inequality that represents the set of integers that satisfy both conditions.The compound inequality is 2 \leq x < 6 .This means we are looking for integers that are both greater than or equal to 2 and less than 6.
List Satisfying Integers: List the integers that satisfy the compound inequality 2 \leq x < 6 .Starting from 2 and going up to but not including 6, we have the integers 2, 3, 4, and 5.These are the integers that are greater than or equal to 2 and less than 6.
Match to Choices: Match the list of integers from Step 3 to the given choices.The list of integers we found is 2,3,4,5.Looking at the choices:(A) 3,4,5,6 - This set includes 6, which should not be included.(B) 3,4,5 - This set does not include 2, which should be included.(C) 2,3,4,5 - This set matches our list exactly.(D) 2,6 - This set does not include 3,4, or 5, and it incorrectly includes 6.