Are the following valid arguments? Explain using the rules of inference.

(a) If you agree with me, then you will vote for me. You vote for me. Therefore, you agree with me.

(b) Everyone who eats fruit every day is healthy. Christine is not healthy. Therefore, Christine does not eat fruit every day.

(c) If I go swimming, then I will stay in the sun too long. If I stay in the sun too long, I will sunburn. Therefore, if I go swimming, then I will sunburn.

(d) If x is a real number with x > 2, then x^2 > 4. Suppose that x <= 2. Then x^2 <= 4.

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