The identity element with respect to the multiplication shown in the diagram below is \(\begin{array}{c|c} \otimes & p & p & r & s \\ \hline p & r & p & r & p \\ q & p & q & r & s\\ r & r & r & r & r\\ s & q & s & r & q\end{array}\)
A. p B. q C. r D. s
Correct Answer: B
Explanation
The identity element (e) under an operation, say \(\otimes\), is the element such that for any given element under the operation, say a, \(a \otimes e = e \otimes a = a\) From the table, q is the identity element. \(p \otimes q = q \otimes p = p\) Same as all through.
