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2. Let X1 and X2 be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T| (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 1 • f = fi and t2 • f = f2.

2. Let X1 and X2 be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T| (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 1 • f = fi and t2 • f = f2.

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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2. Let X1 and X2 be sets. Define functions T1: X1 × 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 aj • f = fj and 12 o f = f2. %3|
Transcribed Image Text:2. Let X1 and X2 be sets. Define functions T1: X1 × 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 aj • f = fj and 12 o f = f2. %3|
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