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91Ó°ÊÓ

Disprove the following statement by giving a counterexample. A counterexample is a specific case that shows a statement is false. Explain.

Every real number has a multiplicative inverse.

Short Answer

Expert verified

0 is the real number which does not has a multiplicative inverse.

Step by step solution

01

- Define real number

Combine sets of rational and irrational number is real number.

02

- Define multiplicative inverse

Let a be the real number such that a·1a=1then 1a is the multiplicative inverse of a

03

- Write counterexample

As, 0 is a real number but there does not exist a number of the form 10

So, 0 does not has a multiplicative inverse.

Thus, every real number does not has a multiplicative inverse.

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