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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 19E

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