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If a, b and c are integers, and a < b, then ac < bc. Is the statement true or false?

Provide proof or a counter example.

Answer 1

Hazel Anglin

#a < b#
#atimes c < b times c#
#ac < bc#
Statement is true

If #a < b#, and we want to prove whether or not #ac < bc#, then we should start out proof with what we know

We know that # a< b#

We then multiply both sides by #c# ie #a times c < b times c #

Results in #ac < bc#

Therefore, it is true for the statement #ac < bc # if and only if #a,b and" c# are integers

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Answer 2

Genesis Allen

The statement is true. When both sides of the inequality (a < b) are multiplied by a positive integer (c), the direction of the inequality remains the same. Thus, (ac < bc) holds true when (a < b) and (c) is a positive integer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

If a, b and c are integers, and a &lt; b, then ac &lt; bc. Is the statement true or false?

Provide proof or a counter example.

If a, b and c are integers, and a < b, then ac < bc. Is the statement true or false?