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The concept of contrapositive proof, a method used to prove conditional statements in mathematics. It discusses the logic behind contrapositive proof, its setup, and provides examples to illustrate its use. The document also contrasts it with direct proof.
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P Q ∼ Q ∼ P P ⇒ Q ∼ Q ⇒∼ P
T T F F T T T F T F F F F T F T T T F F T T T T
(^1) Do not confuse the words contrapositive and converse. Recall from Section 2.4 that the converse of P ⇒ Q is the statement Q ⇒ P, which is not logically equivalent to P ⇒ Q.
n + r for some k,
∈ Z. Then a − b = (kn + r) − ( n + r) = n(k −
). Buta − b = nc (a − b)(a + b) = nc(a + b) a^2 − b^2 = nc(a + b)