2. Let A = {1,2, 3, 4}. (a) Find a function f : A → P(A) so that 1 e f(1). (b) How many functions f: A → P(A) are there so that 1 Ef(1)? Explain. (c) How many functions f: A → P(A) are there so that i E f(i) for all i e A? Explain. (d) How many functions f : A P(A) are there so that i E f(i) for some i E A? Explain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Let A = {1, 2, 3, 4}.
(a) Find a function f : A → P(A) so that 1 E f(1).
(b) How many functions f: A → P(A) are there so that 1 E f(1)? Explain.
(c) How many functions f : A → P(A) are there so that i e f(i) for all i e A? Explain.
(d) How many functions f : A → P(A) are there so that i E f(i) for some i E A? Explain.
Transcribed Image Text:2. Let A = {1, 2, 3, 4}. (a) Find a function f : A → P(A) so that 1 E f(1). (b) How many functions f: A → P(A) are there so that 1 E f(1)? Explain. (c) How many functions f : A → P(A) are there so that i e f(i) for all i e A? Explain. (d) How many functions f : A → P(A) are there so that i E f(i) for some i E A? Explain.
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