Consider the following determinant $$$\Delta = \left| {\matrix{ 1 & a & {bc} \cr 1 & a & {ca} \cr 1 & a & {ab} \cr } } \right|$$$

Which of the following is a factor of $$\Delta $$ ?

The binary relation R = {(1, 1)}, (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4) } on the set A = { 1, 2, 3, 4} is

Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A

$${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\} $$
(a) List the ordered pairs of the equivalence relations induced by $${\Pi _1}$$
(b) Draw the graph of the above equivalence relation.

The number of functions from an $$m$$ element set to an $$n$$ element set is