Determine whether the function f from { a, b, c, d} to { a, b, c, d} is injective (one - to - one), surjective (onto) and/or bijective (one - to - one correspondence) : f(a) = a, f(b) = a,f(c) = b, f(d) = c No points without explanations : 1.Is this function injective? If not, explain: 2. Is this function surjective? If not, explain: 3. Is this function bijective? If not, explain: 4.Is there an inverse for this function? Explain.

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A: Solution is given as: Hope the answer is helpful.

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A: given: we have to determine the value of the composite function:

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A: For the solution follow the next step.

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Q: Prove that f-1 of = Idom f iff f-1 is a function from ran f to dom f.

A: To prove: f-1∘f=Idom f iff f-1 is a function from ran f to dom f

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Q: Let F be a "function" defined on the class

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Q: What is an injective function from a set A into a set B?

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A: We can discard by a counter example

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.