ExplanationThe best way to go about it is to check options one by one..

A) a - b > 0 and c=0 ................ (a - b)c = 0 as c=0 true

B) a=b and c different from 0 .................. a-b=0 so (a - b)c = 0 true

C) a=b and c=0 ........................... both a-b and c terms are 0 so (a - b)c = 0 true

D) a different from b and c=0 .................... c=0 so (a - b)c = 0 holds true

E) a different from b and c different from 0 ........... \(a - b \neq 0\) and \(c \neq 0\) so \((a - b)c \neq 0\).

Hence option E is correct.
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Sandy

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