Suppose f: B → C and g: A → B are functions. Check all the statements that are true: A. If fog is 1-1, then so is f. B. If fog is 1-1 and f is not, then g cannot be onto. C. If fog is 1-1, then so is g. D. If fog is 1-1 and g is not, then f cannot be onto. E. Iff and g are both 1-1, then so is fog. F. None of the above

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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Suppose f: B → C and g: A → B are functions. Check all the statements that are true:
A. If fog is 1-1, then so is f.
B. If fog is
1-1 and f is not, then g cannot be onto.
C. If fog is 1-1, then so is g.
D. If fog is 1-1 and g is not, then f cannot be onto.
E. Iff and g are both 1-1, then so is fog.
F. None of the above
Transcribed Image Text:Suppose f: B → C and g: A → B are functions. Check all the statements that are true: A. If fog is 1-1, then so is f. B. If fog is 1-1 and f is not, then g cannot be onto. C. If fog is 1-1, then so is g. D. If fog is 1-1 and g is not, then f cannot be onto. E. Iff and g are both 1-1, then so is fog. F. None of the above
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