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Injectivity, surjectivity and inverse of a function (CSIR NET Dec 2017 Math.Sci. Part B)
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This is a CSIR NET December 2017 Mathematical Sciences Part B Question.
Question: Which of the following is necessarily true for a function f:X to Y?
1. If f is injective, then there exists a function g:Y to X such that f(g(y))=y for all y ∈ Y.
2. If f is surjective, then there exists a function g:Y to X such that f(g(y))=y for all y ∈ Y.
3. If f is injective and Y is countable, then X is countably finite.
4. If f is surjective and X is uncountable, Y is countably finite.
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Question: Which of the following is necessarily true for a function f:X to Y?
1. If f is injective, then there exists a function g:Y to X such that f(g(y))=y for all y ∈ Y.
2. If f is surjective, then there exists a function g:Y to X such that f(g(y))=y for all y ∈ Y.
3. If f is injective and Y is countable, then X is countably finite.
4. If f is surjective and X is uncountable, Y is countably finite.
Subscribe for more answers and solutions and answer key uploaded in coming days.
Comment below if you want a specific question answered.
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