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Which is the set of integers greater than 3-3 and less than or equal to 00?\newlineChoices:\newline(A){3,2,1,0}\{-3, -2, -1, 0\}\newline(B){3,0}\{-3, 0\}\newline(C){2,1,0}\{-2, -1, 0\}\newline(D){2,1}\{-2, -1\}

Full solution

Q. Which is the set of integers greater than 3-3 and less than or equal to 00?\newlineChoices:\newline(A){3,2,1,0}\{-3, -2, -1, 0\}\newline(B){3,0}\{-3, 0\}\newline(C){2,1,0}\{-2, -1, 0\}\newline(D){2,1}\{-2, -1\}
  1. Identify Inequality: Identify the inequality that represents the condition "greater than 3-3 and less than or equal to 00".\newlineInequality: -3 < x \leq 0
  2. Determine Integers: Determine the set of integers that satisfy the inequality -3 < x \leq 0. The integers greater than 3-3 are 2-2, 1-1, 00, 11, 22, ... However, we also need to consider that xx must be less than or equal to 00. Therefore, we exclude any integers greater than 00.
  3. List Satisfying Integers: List the integers that satisfy both conditions: greater than 3-3 and less than or equal to 00.\newlineThe integers that satisfy both conditions are 2-2, 1-1, and 00.
  4. Match with Choices: Match the set of integers from Step 33 with the given choices.\newlineThe correct set of integers is {2,1,0}\{-2, -1, 0\}, which corresponds to choice (C).

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