Relations Test ...

Given $$\displaystyle A=\left \{ 2, 3 \right \},B=\left \{ 4, 5 \right \},C=\left \{ 5, 6 \right \},$$ find $$\displaystyle A\times \left ( B\cap C \right )=.........$$

$$A$$ and $$B$$ are two sets having $$3$$ and $$5$$ elements respectively and having $$2$$ elements in common. Then the number of elements in $$\displaystyle A\times B$$ is

Let $$R$$ be a relation from a set $$A$$ to a set $$B$$,then

Let $$\displaystyle A=\left \{ 1, 2, 3, 4, 5 \right \}, B=\left \{ 2, 3, 6, 7 \right \}.$$ Then the number of elements in $$\displaystyle \left ( A\times B \right )\cap \left ( B\times A \right )$$ is

If $$\displaystyle A=\left \{ a, b, c \right \},B=\left \{ c, d, e \right \},C=\left \{ a, d, f \right \}$$, then $$A\times \left ( B\cup C \right )$$ is

If $$\displaystyle A=\left \{ 2, 4 \right \}$$ and  $$B\left \{ 3, 4, 5 \right \},$$ then $$\displaystyle \left ( A\cap B \right )\times \left ( A\cup B \right )$$ is

If $$\displaystyle X= \left \{ 1,2,3,4,5 \right \}, Y= \left \{ 1,3,5,7,9 \right \}$$ determine which of the following sets are mappings, relations or neither from A to B:

If $$\displaystyle A=\left \{ 1, 2, 3 \right \}$$ and $$B=\left \{ 3, 8 \right \},$$ then $$\displaystyle \left ( A\cup B \right )\times \left ( A\cap B \right )$$ is

Let $$A$$ and $$B$$ be two finite sets having $$m$$ and $$n$$ elements respectively. Then the total number of mapping from $$A$$ to $$B$$ is:

Let $$R$$ be a reflexive on a finite set $$A$$ having $$n$$ elements, and let there be $$m$$ ordered pairs in $$R$$. Then