Question

list the ordered pairs in the equivalence relations R induced by these partitions of p { {1} , {3} , { 2,4,5,6} rt he set of { 1,2,3,4,5,6}

Answer 1

Let us list the ordered pairs in the equivalence relations $R$ induced by the partition $P= \{ \{1\} , \{3\} , \{ 2,4,5,6\}\}$ on the set $\{ 1,2,3,4,5,6\}.$

Recall that $(a,b)\in R$ if and only if $a,b\in A$ for some $A\in P.$

It follows that

$R=\{(1,1),(3,3),(2,2),(2,4),(2,5),(2,6),(4,2),(4,4),(4,5),(4,6),\\ (5,2),(5,4),(5,5),(5,6),(6,2),(6,4),(6,5),(6,6)\}.$