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2. Let X1 and X2 be sets. Define functions T1: X1 x X2 → X1, T2 : X, × X, → X2 by T (X1, 12) = #1, T72 (#1, #2) = #2 (1 € X1, 12 E X2). Also let A be a set, and let f: A →X1, f2: A → X2 be functions. Prove that there is exactly one function f : A→ X1 × X2 such that T1 of= fi and T2 of= f2-

2. Let X1 and X2 be sets. Define functions T1: X1 x X2 → X1, T2 : X, × X, → X2 by T (X1, 12) = #1, T72 (#1, #2) = #2 (1 € X1, 12 E X2). Also let A be a set, and let f: A →X1, f2: A → X2 be functions. Prove that there is exactly one function f : A→ X1 × X2 such that T1 of= fi and T2 of= 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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Sophie McGonigal igation H08: Hand-in problems shboard 1. Let f: X → Y and g : Y X be maps between sets. Suppose that go f is equal to the identity map idx : XX. Does it follow that fo gis equal to the identity map idy : Y Y? Give a proof or a counterexample. Site home Site pages My courses 2. Let X1 and X2 be sets. Define functions - CAP 2021-22 T: X¡ x X2 → X1, Tg: X, × X, → X, www.learn.ed 87637 _1 by T1 (11, x2) = x1, 72 (21, #2) = x2 > Participants O Badges E Competencies (21 € X1, 12 E X2). Also let A be a set, and let 田 Grades fi : A → X1, f2: A → X2 > General be functions. > Research > 1. Sets, numbers and proof qualifiers Prove that there is exactly one function f : A → X1 × X2 such that T of= fi and T2 of= f2. > 2. Inequalities, (You may find it helpful to draw a diagram showing all the sets and functions involved.) Mathematical Induction Last modified: Thursday, 17 March 2022, 12:47 AM > 3. Upper Bounds,
Transcribed Image Text:Sophie McGonigal igation H08: Hand-in problems shboard 1. Let f: X → Y and g : Y X be maps between sets. Suppose that go f is equal to the identity map idx : XX. Does it follow that fo gis equal to the identity map idy : Y Y? Give a proof or a counterexample. Site home Site pages My courses 2. Let X1 and X2 be sets. Define functions - CAP 2021-22 T: X¡ x X2 → X1, Tg: X, × X, → X, www.learn.ed 87637 _1 by T1 (11, x2) = x1, 72 (21, #2) = x2 > Participants O Badges E Competencies (21 € X1, 12 E X2). Also let A be a set, and let 田 Grades fi : A → X1, f2: A → X2 > General be functions. > Research > 1. Sets, numbers and proof qualifiers Prove that there is exactly one function f : A → X1 × X2 such that T of= fi and T2 of= f2. > 2. Inequalities, (You may find it helpful to draw a diagram showing all the sets and functions involved.) Mathematical Induction Last modified: Thursday, 17 March 2022, 12:47 AM > 3. Upper Bounds,
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