True or True #8

Algebra Level 2

True or False?

If a c = b d and c = d , then it is certain that a = b . \text{If } ac = bd \text{ and } c = d, \text{ then it is certain that } a = b.

True False

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5 solutions

Discussions for this problem are now closed

a c = b d ac = bd and c = d c = d a = b \Rightarrow a = b , provided that c c and d d are not equal to 0.

Therefore, the true statement is " If a c = b d ac = bd and c = d c = d , then a a is NOT always equal to b b . For example, If 3 × 0 = 2 × 0 3 \times 0 = 2 \times 0 and 0 = 0 0 = 0 , then 3 = 2, which is wrong.

William Isoroku
Dec 3, 2014

If c = d = 0 c=d=0 , then a a and b b could be any number.

Sakshi Taparia
Dec 18, 2014

if c=d=0, they can not be cancelled. In that case, a may or may not be equal to b

Bhavik Knight
Dec 12, 2014

condition is c=d but must not = 0

Fox To-ong
Dec 16, 2014

if c = d,unless provided that a = b then both products should always be equal, but if not then a should not be equal to the product of c and d, then a should not be equal to b. FALSE

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