Either provide an informal proof of OR a counterexample to each of the following. If g and h are relations on R x R, and g and g ∘ h are both one-to-one, then h is one-to-one. If f is a function from finite set A to finite set B and |A| = |B|, then f is one-to-one if and only if f is onto.

Either provide an informal proof of OR a counterexample to each of the following. If g and h are relations on R x R, and g and g ∘ h are both one-to-one, then h is one-to-one. If f is a function from finite set A to finite set B and |A| = |B|, then f is one-to-one if and only if f is onto.

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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Either provide an informal proof of OR a counterexample to each of the following.

If g and h are relations on R x R, and g and g ∘ h are both one-to-one, then h is one-to-one.
If f is a function from finite set A to finite set B and |A| = |B|, then f is one-to-one if and only if f is onto.

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