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2. Prove that the function f : R? → IR defined by f(x, y) = 1- a2 – 4y? is neither injective nor surjective.

2. Prove that the function f : R? → IR defined by f(x, y) = 1- a2 – 4y? is neither injective nor surjective.

Advanced Engineering Mathematics
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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answer item 2 only.
1. Let be a function from A to B, and X, Y C B. Show that f-'(XnY) = f-'(X)nf-(Y). 2. Prove that the function f: R² → R defined by f(x, y) = 1 – x² – 4y? is neither injective nor surjective. 3. Let A {8k + 7 : k e Z} and B = {4j + 3 : je Z}. Show that A C B. 4. Let X, Y and Z be subsets of the universal set U. Prove using ONLY definitions (logical connectives) that X\ (Y \ Z) = (X n z)U (X \Y).
Transcribed Image Text:1. Let be a function from A to B, and X, Y C B. Show that f-'(XnY) = f-'(X)nf-(Y). 2. Prove that the function f: R² → R defined by f(x, y) = 1 – x² – 4y? is neither injective nor surjective. 3. Let A {8k + 7 : k e Z} and B = {4j + 3 : je Z}. Show that A C B. 4. Let X, Y and Z be subsets of the universal set U. Prove using ONLY definitions (logical connectives) that X\ (Y \ Z) = (X n z)U (X \Y).
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