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All four of the statements are true. Remember, the only way for an implication to be false is for the if part to be true and the then part to be false.

  1. Here both the hypothesis and the conclusion are true, so the implication is true. It does not matter that there is no meaningful connection between the true mathematical fact and the fact about horses.

  2. Here the hypothesis is false and the conclusion is true, so the implication is true.

  3. I have no idea what the 7624th digit of \(\pi\) is, but this does not matter. Since the hypothesis is false, the implication is automatically true.

  4. Similarly here, regardless of the truth value of the hypothesis, the conclusion is true, making the implication true.

in-context