Write:

a. Rational number that does not have a reciprocal.

b. Rational numbers that are equal to their reciprocals.

c. The rational number is equal to its negative.

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Undefined, -1,0

Defined, -1,-0

Undefined, 1,-0

None of these

answer is A.

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Detailed Solution

Concept: (i) There is no reciprocal for a rational number.
The rational number 0 (zero) has no reciprocal since it is undefined (∞).
0/0 = Unknown
(ii) The rational numbers equivalent to their reciprocals
The rational integers 1 and -1 are equivalent to their reciprocals.
The reciprocal of 1 is 1/1 = 1, while the reciprocal of -1 is 1/(-1) = -1.
(iii) The rational number is equal to its inverse.
The rational number 0 is equivalent to its inverse.
The number 0 is neither positive nor negative. As a result, 0 equals -0.
Hence, the correct option is (1).

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