Question

Let $A=\{1,2,3\}$. Which of the following is not an equivalence relation on A?

• A. $\left\{\right(1,1),(2,2),(3,3\left)\right\}$
• B. $\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1\left)\right\}$
• C. $\left\{\right(1,1),(2,2),(3,3),(2,3),(3,2\left)\right\}$
• D. $\left\{\right(1,1),(2,1\left)\right\}$

Answer 1

The correct option is D $\left\{\right(1,1),(2,1\left)\right\}$

every relation in options follow the equivalence property.

but in fourth option this option only contains two elements $\left[\right[1,1],[2,1\left]\right]$

this option doesn't satisfy reflexive i.e., doesn't contain all $(a,a)$ type $(2,2),(3,3)$

Not symmetric i.e., doesn't contain this type of elements $(1,2)$ missing

and as well transitive.

and all others options satisfy these relations.