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Read this statement: 'Every square is a rectangle.' Which of the four statements below says exactly the same thing, so that it must be true whenever the given statement is true?

Competition practiceReasoning & Mental Ability
  • AEvery rectangle is a square.
  • BAnything that is not a rectangle is not a square.
  • CAnything that is not a square is not a rectangle.
  • DNo rectangle is a square.

Step-by-Step Solution

Turning 'if A then B' around and negating both parts gives 'if not B then not A', which always carries exactly the same meaning. Here that reads: anything that is not a rectangle cannot be a square. The traps: 'every rectangle is a square' simply swaps the two parts and is plainly false; 'anything that is not a square is not a rectangle' negates without swapping and is false too (a 4 by 7 rectangle is not a square); and 'no rectangle is a square' contradicts the original outright.
Answer: B) Anything that is not a rectangle is not a square.

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