   Chapter 12.4, Problem 53E

Chapter
Section
Textbook Problem

# Suppose that a ≠ 0.(a) If a · b = a · c, does it follow that b = c?(b) If a × b = a × c, does it follow that b = c?(c) If a · b = a ·     c and a × b = a × c, does it follow that b = c?

(a)

To determine

To analyze: If ab=ac , does it follow that b=c .

Explanation

Given data:

a0 .

Consider ab=ac and simplify the equation as follows.

ab=acabac=0a(bc)

(b)

To determine

To analyze: If a×b=a×c , does it follow that b=c .

(c)

To determine

To analyze: If ab=ac and a×b=a×c , does it follow that b=c .

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