Q2Discrete Mathematics Structure

Question

Let A = {1, 2, 3, 4} and consider the partition P = {{1, 2, 3}, {4}} of A. Obtain the equivalence relation R on A determined by P.

Answer 1

The equivalence relation $R$ determined by a partition is the union of Cartesian products of each set in the partition with itself.

$R = ({1, 2, 3} \times {1, 2, 3}) \cup ({4} \times {4})$

$R = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 4)}$

Question