Question

$R=(1,2),(2,3),\left(34\right)$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is

• A. 5
• B. 7
• C. 9
• D. 11

Answer 1

Answer: (C)

9

$\begin{array}{c}\text{solution:}R=(1,2),(2,3),(3,4)\\ \text{To make it an equivalence relation, we need}\\ \text{to make it Reflexive, symmetric and transitive}\\ \text{at the same time.}\\ \text{Elements needed to make it Reflexive are}\\ (1,1),(2,2),(3,3),(4,4)\end{array}$

$\begin{array}{c}\text{Elements related to make it symmetric are}\\ (2,1),(3,2),(4,3)\\ \text{Elements needed to make it transitive are}\\ (1,3)\text{,}(2,4)\\ \text{so total number of terms required are}9\\ \text{Answer: option (c)}\end{array}$