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.

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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”.

Question

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.
5. Can composition be performed? fof(x)? If not, explain.

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