 # Let A = R − { 0 } , the set of all nonzero real numbers, and consider the following relations on A × A . Decide in each case whether R is an equivalence relation, and justify your answers. ( a , b ) R ( c , d ) if and only if a d = b c . ( a , b ) R ( c , d ) if and only if a b = c d . ( a , b ) R ( c , d ) if and only if a 2 + b 2 = c 2 + d 2 . ( a , b ) R ( c , d ) if and only if a − b = c − d . ### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
Publisher: Cengage Learning,
ISBN: 9781285463230 ### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
Publisher: Cengage Learning,
ISBN: 9781285463230

#### Solutions

Chapter
Section
Chapter 1.7, Problem 15E
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