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What does the set \{x | x > 7\} represent?\newlineChoices:\newline(A)all numbers equal to 77 \newline(B)all numbers greater than or equal to 77 \newline(C)all numbers greater than 77 \newline(D)all numbers less than or equal to 77

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Full solution

Q. What does the set {x∣x>7}\{x | x > 7\} represent?\newlineChoices:\newline(A)all numbers equal to 77 \newline(B)all numbers greater than or equal to 77 \newline(C)all numbers greater than 77 \newline(D)all numbers less than or equal to 77
  1. Understand set notation: Understand the set notation. The set {x | x > 7} uses the inequality sign '>', which means 'greater than'.
  2. Match notation to description: Match the set notation to the correct choice. We are looking for the description that matches the set of all numbers that are greater than 77.
  3. Eliminate incorrect choices: Eliminate incorrect choices. Choice (A) suggests all numbers equal to 77, which does not match the 'greater than' sign. Choice (D) suggests all numbers less than or equal to 77, which is the opposite of what we want. Therefore, both (A) and (D) are incorrect.
  4. Compare remaining choices: Compare the remaining choices. Choice (B) says 'all numbers greater than or equal to 77', but our set does not include 77 itself, it is only greater than 77. Choice (C) says 'all numbers greater than 77', which exactly matches our set notation.
  5. Select correct answer: Select the correct answer. Based on the set notation {x | x > 7}, the correct choice is (C) all numbers greater than 77.

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