Prove that if R, S, and T are nonempty sets, then R×T ⊆ S×T if and only if R ⊆ S.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 2TFE: Label each of the following statements as either true or false. 2. for all nonempty sets A and B.
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Prove that if R, S, and T are nonempty sets, then R×T ⊆ S×T if and only if R ⊆ S.

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