a.Prove that {12a+ 4b | a, b ∈ Z}={4c |c ∈ Z}. (b) Prove that{20a+ 16b|a,...

a.Prove that {12a+ 4b | a, b ∈ Z}={4c |c ∈ Z}.

(b) Prove that{20a+ 16b|a, b ∈ Z}={28m+ 32n|m, n ∈ Z}.

(c) Leta, b ∈ Z−{0}. Prove that{x ∈ Z |ab divides x}⊆{x ∈ Z |a divides x}.

(d) Prove that{16n|n∈Z}⊆{2n|n ∈ Z}.

Expert Solution

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Colby Messinger answered 6 months ago

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Question

a.Prove that {12a+ 4b | a, b ∈ Z}={4c |c ∈ Z}. (b) Prove that{20a+ 16b|a,...

Solutions

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