Mathematics 2000 JAMB Past Questions - Question 14: find the inverse of p under the binary operation *defined by p*q=p+q.where p and q are real numbers and zero is the identity.

Correct Answer

A

Explanation

To find the inverse of an element under a binary operation, you need to find an element that, when combined with the original element under the operation, gives the identity element. In this case, the identity element is zero. To find the inverse of p under the binary operation * defined by p*q = p + q, we need to find a real number q such that p * q = 0, where 0 is the identity element.Let's solve for q:p * q = p + qTo find the inverse, we want the result to be 0. Therefore, we can set p + q = 0 and solve for q:q = -pSo, the inverse of p under the binary operation * is -p.Let's find the inverse of an element "p" under the binary operation "," where p and q are real numbers, and the operation is defined as pq = p + q.We need to find an element x such that:p * x = 0Using the definition of the binary operation:p + x = 0Now, solve for x:x = pSo, the inverse of an element "p" under this operation is "-p." In other words, for any real number "p," the element "-p" is its inverse under the operation "*", as (p * -p) = p + (-p) = 0, which is the identity element.