Question

The number 0 is not the reciprocal of any number.
(a) True
(b) False
(c) Ambiguous
(d) None

Answer 1

Hint: The reciprocal of a number is the multiplicative inverse of that number and we know that if a number’s multiplicative inverse is 0 then the number is not defined so accordingly choose the correct options given in the question.

Complete step-by-step answer:
We are asked to comment on the statement given in the problem which is “The number 0 is not the reciprocal of any number”.
Let us assume that the number 0 is the reciprocal of “a”. This means that 0 is the multiplicative inverse of “a” or we can write as:
$a\times 0=1$ ………..Eq. (1)
If the above equation will be true then “a” is equal to $\dfrac{1}{0}$ which is implying that the number we have assumed is not defined. And we cannot take the reciprocal of an undefined number. From this statement we can say that the above equation does not hold true. We can also say that the reciprocal of “a” could not be 0.
From the above discussion we have determined that the statement given in the question which is “The number 0 is not the reciprocal of any number” is true.
Hence, the correct option is (a).

Note: In the eq. (1) given in the solution:
$a\times 0=1$
You might tempt to divide “a” on both the sides if you divide it then the value of “a” will be:
$0=\dfrac{1}{a}$
On rearranging the above equation you will get:
$a=\dfrac{1}{0}$
From the above, we got “a” as an undefined number and this whole logic is unjustified because you cannot divide the undefined number.