Let n be a non-negative integer. Prove that if n is a multiple of 3, then...

 

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Let n be a non-negative integer. Prove that if n is a multiple of 3, then n is a multiple of 3. Let n be a non-negative integer. Prove that if n is a not a multiple of 3, then n is 1 more than a multiple of 3. Let T(n) be the predicate "n is a multiple of 3", and let S(n) be the predicate "n is a multiple of 3". Taking the domain for n to be the non-negative integers, determine whether the following propositions are true or false, and give proofs of your assertions. (T(n) = S(n)). En (T(n) A-S(n)). (S(n) T(n)). n (S(n)T(n)). (3) (4) (5) (6) You may of course refer to anything you proved in earlier parts without having to copy over the proof. Let n be a non-negative integer. Prove that if n is a multiple of 3, then n is a multiple of 3. Let n be a non-negative integer. Prove that if n is a not a multiple of 3, then n is 1 more than a multiple of 3. Let T(n) be the predicate "n is a multiple of 3", and let S(n) be the predicate "n is a multiple of 3". Taking the domain for n to be the non-negative integers, determine whether the following propositions are true or false, and give proofs of your assertions. (T(n) = S(n)). En (T(n) A-S(n)). (S(n) T(n)). n (S(n)T(n)). (3) (4) (5) (6) You may of course refer to anything you proved in earlier parts without having to copy over the proof.