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The main thing to realize is that we don’t know the colors of these two shapes, but we do know that we are in one of three cases: We could have a blue square and green triangle. We could have a square that was not blue but a green triangle. Or we could have a square that was not blue and a triangle that was not green. The case in which the square is blue but the triangle is not green cannot occur, as that would make the statement false.

  1. This must be false. In fact, this is the negation of the original implication.

  2. This might be true or might be false.

  3. True. This is the contrapositive of the original statement, which is logically equivalent to it.

  4. We do not know. This is the converse of the original statement. In particular, if the square is not blue but the triangle is green, then the original statement is true but the converse is false.

  5. True. This is logically equivalent to the original statement.

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