Let S be the set of all rational numbers of the form m/n, where m ∈ Z and n = 1,2,3. Prove that * on S defined by a*b = ab is not a binary operation.

Question

Philoid · Accepted Answer

Given that * is an operation that is valid on the set S which consists of all rational numbers of the form , here m∈Z and n = 1,2,3 and is defined by a*b = ab.

According to the problem it is given that on applying the operation * for two given numbers in the set ‘S’ it gives a number in the set ‘S’ as a result of the operation.

⇒ a*b∈S ...... (1)

Since a∈S and b∈S,

Let us take the values of then,

⇒

⇒ as 9∉n.

∴ The operation ‘*’ does not define a binary operation on ‘S’.

Let S be the set of all rational numbers of the form m/n, where m∈Z and n = 1,2,3. Prove that * on S defined by a*b = ab is not a binary operation.