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necessary-conditionssufficient-conditionslogic-concepts

Is This Condition Necessary or Sufficient?

Problem Statement

Consider: 'Being a square is a condition for being a rectangle.' Is this condition necessary, sufficient, both, or neither?

Answer

Sufficient but not necessary

Step-by-Step Explanation

  1. 1

    First, let's clarify the relationship: All squares are rectangles, but not all rectangles are squares.

  2. 2

    Necessary condition: Must be true for the conclusion to be true.

  3. 3

    Sufficient condition: If true, guarantees the conclusion is true.

  4. 4

    Question: Is 'being a square' necessary or sufficient for 'being a rectangle'?

  5. 5

    Sufficient: If something is a square, it IS a rectangle. ✓

  6. 6

    Necessary: Must something be a square to be a rectangle? No — rectangles can have unequal sides.

  7. 7

    Therefore: Being a square is SUFFICIENT but NOT NECESSARY for being a rectangle.

  8. 8

    Example: A 2×4 rectangle is a rectangle but not a square.