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Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A ⊆ B and B ⊆ D, then A ⊆ C" is:

1. (1) If A ⊄ C, then A ⊆ B and B ⊆ D
2. (2) If A ⊄ C, then A ⊄ B and B ⊆ D
3. (3) If A ⊄ C, then A ⊄ B or B ⊄ D
4. (4) If A ⊆ C, then B ⊄ A or D ⊄ B

Correct answer: (3) If A ⊄ C, then A ⊄ B or B ⊄ D

Solution

The contrapositive of a conditional statement reverses and negates both the hypothesis and conclusion. In this case, if A is not a subset of C, it logically follows that either A cannot be a subset of B or B cannot be a subset of D, which aligns with option (3).

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