How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b. f(1) # 1 or f(2) # 2 (or both)? c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective? d. f is surjective, but Va E {1,2,...,4}, f(x) = x? A A J F

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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How many functions f: {1, 2, 3, 4} → {1, 2, 3, 4} are there satisfying:
a. f(1) = 1 or f(2)= 2 (or both)?
b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)?
c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective?
d. f is surjective, but Vx = {1, 2,...,4}, ƒ(x) ‡ x?
JI
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FI
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Transcribed Image Text:How many functions f: {1, 2, 3, 4} → {1, 2, 3, 4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)? c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective? d. f is surjective, but Vx = {1, 2,...,4}, ƒ(x) ‡ x? JI - FI -
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