Let S be the set of all odd integers, and define a function f: Z → S as follows: f(n) = 2n + 1 for all integers n. %3D Prove that f is one-to-one and onto.

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A: True

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Q: 15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c)…

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Q: Let function f: Z Z be defined as follows; 1 x is odd f(x) = . x² + 2 x is even The functionf is .…

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Q: 5. Determine whether the function f : Z × Z →Z is onto if a) f (m, n) = m² + n² b)f (m, n) = m³

A: See the solution.

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A: We will prove this by contradiction.

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Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

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A: here we can use contradiction to prove this stetements.

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A: Please comment if you need any clarification. IF you find my answer useful put thumbs up. Thank you.

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A: Here we use IVP theorem to prove this

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