Show that none of the operations given above has identity.
Answer
An element e ∈ Q will be the identity element for the operation * if a * e = a = e * a, a ∈Q.
However, there is no such element e ∈ Q with respect to each of the six operations satisfying the above condition.
Thus, none of the six operations has identity.
An element e ∈ Q will be the identity element for the operation * if a * e = a = e * a, a ∈Q.
However, there is no such element e ∈ Q with respect to each of the six operations satisfying the above condition.
Thus, none of the six operations has identity.
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