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How many functions f: {1,2,3,4} → a. ƒ(1) = 1 or ƒ(2) = 2 (or both)? → {1, 2, 3, 4} are there satisfying: b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)? c. ƒ(1) ‡ 1 and fƒ(2) ‡ 2, and ƒ is injective? d. f is surjective, but Vâ € {1, 2,...,4}, ƒ(x) ‡ x?

How many functions f: {1,2,3,4} → a. ƒ(1) = 1 or ƒ(2) = 2 (or both)? → {1, 2, 3, 4} are there satisfying: b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)? c. ƒ(1) ‡ 1 and fƒ(2) ‡ 2, and ƒ is injective? d. f is surjective, but Vâ € {1, 2,...,4}, ƒ(x) ‡ x?

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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Correct Answer 98 +98 97 8.98 +9.8.97-8.8.97 9! — (8! + 8! — 7!) 9! - 229384
Transcribed Image Text:Correct Answer 98 +98 97 8.98 +9.8.97-8.8.97 9! — (8! + 8! — 7!) 9! - 229384
How many functions f : {1, 2, 3, 4} → {1, 2, 3, 4} are there satisfying: a. ƒ(1) = 1 or ƒ(2) = 2 (or both)? b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)? ID c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective? -> d. f is surjective, but Væ € {1, 2,...,4}, ƒ(x) ‡ x?
Transcribed Image Text:How many functions f : {1, 2, 3, 4} → {1, 2, 3, 4} are there satisfying: a. ƒ(1) = 1 or ƒ(2) = 2 (or both)? b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)? ID c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective? -> d. f is surjective, but Væ € {1, 2,...,4}, ƒ(x) ‡ x?
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