Define F: R x R → R × R as follows: F(x, y) = (3y – 1,1 – a) for all (x, y) in R × R. (a) F(0,0) = ? F(1, 4) = ? (b) Is F one-to-one? Prove or give a counterexample. (c) Is F onto? Prove or give a counterexample. (d) Is F a one-to-one correspondence? If not, explain why not. If yes, find F-1.

Define F: R x R → R × R as follows: F(x, y) = (3y – 1,1 – a) for all (x, y) in R × R. (a) F(0,0) = ? F(1, 4) = ? (b) Is F one-to-one? Prove or give a counterexample. (c) Is F onto? Prove or give a counterexample. (d) Is F a one-to-one correspondence? If not, explain why not. If yes, find F-1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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