Sets- I Starter Quiz-1

Let A = {1, 2, 3, 4, 5}, B = {1, 2}, C = {3, 4, 5} and 𝜑 denote the null set. If A × B denotes the cartesian product of the sets A and B , then (A × B) ⋂ (A × C) is?

If A = {3, 2, 6} and B = {1, 2, 3}, find number of elements in cartesian product of A × B?

If A is a set with 3 elements, then find the number of relations possible on set A which are asymmetric but not symmetric?

Consider the following Statements.

a) If a relation ‘R’ on a set of ‘A’ is symmetric and transitive then ‘R’ is reflexive.

b) If a relation ‘R’ on a set of ‘A’ is irreflexive and transitive then ‘R’ is antisymmetric.

c) If ‘R’ and ‘S’ are antisymmetric relations on a set ‘A’ then (R Union S) and (R intersection S) are also antisymmetric.

d) If ‘R’ and ‘S’ are transitive relations, then R intersection S is always transitive but R union S need not be transitive.

Find the number of incorrect statements ___________?

How many subsets of {1, 2, 3 … 11} contain at least one even integer?

How many relations on a set with 3 elements are neither reflexive nor irreflexive _________?