## Logic, proof, and sets |

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3yVx A U B arbitrary Assume P(k B U C BASIS STEP C(P v Q calculus Commutative Law Conditional Proof consider contrapositive converges Deduce P(k deduce Q defined Definition element equivalence classes equivalence relation EXAMPLE Exercise Set f is continuous f is differentiable false Find function f graph Hence Hint i=l i=l i=l ieF Iff-string INDUCTION STEP integer logical symbolism mathematical induction mathematical system mathematician mode of proof modus ponens natural number non-empty odd integer ordered pairs partition proof by contradiction prove a sentence Prove P(l Prove the following Q is true quantifier rational number reflexive replacement set of P(x set theory simplified negation solution set subsets Suppose symmetric tautology Theorem triangle truth table truth value type VxP(x universal set valid argument VnP(n Vx3y VxQ(x VxVy x e Q x|x e