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Inverse in Binary Operation

A binary oper...

Question

A binary operation can result in an inverse for a number even in the absence of an identity

A

True

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B

False

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Q. Q⁺ is the set of all positive rational numbers with the binary operation * defined by

a * b = \frac{a b}{2}

for all a, b ∈ Q⁺. The inverse of an element a ∈ Q⁺ is
(a) a

(b)

\frac{1}{a}

\frac{2}{a}

\frac{4}{a}

Q. On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all a, b ∈ Z. Write the inverse of 4.

Q. For the binary operation ×₁₀ on set S = {1, 3, 7, 9}, find the inverse of 3.

Q. On the set Q⁺ of all positive rational numbers a binary operation * is defined by

a * b = \frac{a b}{2} for all, a, b \in Q^{+}

. The inverse of 8 is
(a)

\frac{1}{8}

\frac{1}{2}

Q. For the binary operation multiplication modulo 10 (×₁₀) defined on the set S = {1, 3, 7, 9}, write the inverse of 3.

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