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If the statement 'All squares are rectangles' is true, which of the following mu

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Question: If the statement \'All squares are rectangles\' is true, which of the following must also be true?

Options:

  1. All rectangles are squares.
  2. Some rectangles are not squares.
  3. No rectangles are squares.
  4. Some squares are not rectangles.

Correct Answer: Some rectangles are not squares.

Solution: 

If all squares are rectangles, it implies that there are rectangles that are not squares, thus some rectangles are not squares.

If the statement 'All squares are rectangles' is true, which of the following mu

Practice Questions

Q1
If the statement 'All squares are rectangles' is true, which of the following must also be true?
  1. All rectangles are squares.
  2. Some rectangles are not squares.
  3. No rectangles are squares.
  4. Some squares are not rectangles.

Questions & Step-by-Step Solutions

If the statement 'All squares are rectangles' is true, which of the following must also be true?
  • Step 1: Understand the statement 'All squares are rectangles'. This means every square fits the definition of a rectangle.
  • Step 2: Recognize that if all squares are rectangles, there can be rectangles that are not squares. This is because rectangles can have different shapes, not just squares.
  • Step 3: Conclude that since there are rectangles that are not squares, it must be true that some rectangles are not squares.
  • Logical Implication – Understanding how the truth of one statement (all squares are rectangles) can imply the truth of another statement (some rectangles are not squares).
  • Set Theory – Recognizing the relationships between different sets (squares as a subset of rectangles).
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