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What does the set \{x | x > 7\} represent?\newlineChoices:\newline(A)all numbers greater than 77 \newline(B)all numbers equal to 77 \newline(C)all numbers less than or equal to 77 \newline(D)all numbers greater 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 greater than 77 \newline(B)all numbers equal to 77 \newline(C)all numbers less than or equal to 77 \newline(D)all numbers greater than or equal to 77
  1. Understand set notation: Understand the set notation. The set {x | x > 7} uses the inequality sign '>', which represents ＂greater than.＂
  2. Determine inequality meaning: Determine the meaning of the inequality sign in the context of the set. The inequality x > 7 means that we are looking for all numbers that are greater than 77.
  3. Match inequality with choices: Match the meaning of the inequality with the given choices. Since we are looking for numbers greater than 77, we need to find the choice that corresponds to this description.
  4. Evaluate given choices: Evaluate the choices given:\newline(A) all numbers greater than 77 - This matches our set notation \{x | x > 7\}.\newline(B) all numbers equal to 77 - This does not match because our set notation specifies numbers greater than 77, not equal to 77.\newline(C) all numbers less than or equal to 77 - This is the opposite of what we are looking for.\newline(D) all numbers greater than or equal to 77 - This includes 77 itself, which is not included in our set notation.
  5. Select correct choice: Select the correct choice based on the evaluation. Choice (A) is the correct answer because it represents all numbers greater than 77, which is exactly what the set \{x | x > 7\} denotes.

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