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Which is the set of integers greater than or equal to 22 and less than 66?\newlineChoices:\newline(A) {3,4,5}\{3, 4, 5\}\newline(B) {3,4,5,6}\{3, 4, 5, 6\}\newline(C) {2,3,4,5}\{2, 3, 4, 5\}\newline(D) {2,6}\{2, 6\}

Full solution

Q. Which is the set of integers greater than or equal to 22 and less than 66?\newlineChoices:\newline(A) {3,4,5}\{3, 4, 5\}\newline(B) {3,4,5,6}\{3, 4, 5, 6\}\newline(C) {2,3,4,5}\{2, 3, 4, 5\}\newline(D) {2,6}\{2, 6\}
  1. Define Inequality: Let's first define the inequality that represents the set of integers greater than or equal to 22 and less than 66. We need to use two inequality signs: one for "greater than or equal to" (\geq) and one for "less than" (<).
  2. Write Set Notation: Now, let's write down the set notation that includes all integers xx such that 2 \leq x < 6. This means we are looking for integers that are at least 22 but strictly less than 66.
  3. List Integers: We list out the integers that satisfy the inequality 2 \leq x < 6. These integers are 22, 33, 44, and 55. The number 66 is not included because the inequality is strictly less than 66.
  4. Match with Choices: We match our list of integers 2,3,4,5{2, 3, 4, 5} with the given choices to find the correct set.\newline(A) 3,4,5{3, 4, 5} does not include 22, so it is not correct.\newline(B) 3,4,5,6{3, 4, 5, 6} includes 66, which should not be in the set, so it is not correct.\newline(C) 2,3,4,5{2, 3, 4, 5} includes all the integers that satisfy the inequality, so it is correct.\newline(D) 2,6{2, 6} does not include 33, 44, or 55, so it is not correct.

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