Applied Grand Test 2

Question

Consider the equivalence relation R induced by the partition P={{1},{3},{2,4,5,6}} of set A={1,2,3,4,5,6}.

The number of ordered pairs in R is ____

Answer 1

Answer = 1^2 +1^2 + 4^2 = 1+ 1+ 16 =18

Pairs for partition {1} = {1}x{1}={(1,1)};

Pairs for partition {3} = {3}x{3}={(3,3)};

Pairs for partition {2,4,5,6} = {2,4,5,6}x{2,4,5,6}={16 pairs};

The number of orderd pairs in R will be 18.