2. Let X and X, be sets. Define functions T1 : X1 x X2 → X1, T2 : X1 × X2 → X2 by T1(X1, X2) = X1, T2(X1, x2) = x2 (x1 E X1, x2 e X2). Also let A be a set, and let fi : A → X1, f2 : A → X2 be functions. Prove that there is exactly one function f : A → X1× X2 such that ë¡ • f = fj and a2 • f = f2.
2. Let X and X, be sets. Define functions T1 : X1 x X2 → X1, T2 : X1 × X2 → X2 by T1(X1, X2) = X1, T2(X1, x2) = x2 (x1 E X1, x2 e X2). Also let A be a set, and let fi : A → X1, f2 : A → X2 be functions. Prove that there is exactly one function f : A → X1× X2 such that ë¡ • f = fj and a2 • f = f2.
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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Transcribed Image Text:2. Let X and X, be sets. Define functions
T1 : X1 x X2 → X1,
T2 : X1 × X2 → X2
by
T1(X1, X2) = X1,
T2(X1, x2) = x2
(x1 E X1, x2 e X2). Also let A be a set, and let
fi : A → X1,
f2 : A → X2
be functions.
Prove that there is exactly one function f : A → X1× X2 such that ë¡ • f = fj and a2 • f = f2.
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