Relations Test ...

If $$\displaystyle A= \left \{ a,b,c,d \right \}, B= \left \{ 1,2,3 \right \}$$ find whether or not the following sets of ordered pairs are relations from $$A$$ to $$B$$ or not.
$$\displaystyle R_{1}= \left \{ \left ( a,1 \right ), \left ( a,3 \right ) \right \}$$
$$\displaystyle R_{2}= \left \{ \left ( a,1 \right ), \left ( c,2 \right ), \left ( d,1 \right ) \right \}$$
$$\displaystyle R_{3}= \left \{ \left ( a,1 \right ), \left ( b,2 \right ), \left ( 3,c \right ) \right \}.$$

If ,$$(x-1, y+2)= (7, 5)$$ then values of $$x$$ and $$y$$ are

Ordered pairs (a, 3) and (5, x) are equal ,the values of $$a$$ and $$x$$ are

If $$(x, y) = (3, 5)$$ ; then values of $$x$$  and $$y $$ are 

Given $$M = (0, 1, 2)$$ and $$N = (1, 2, 3)$$. Find $$(N - M) \times (N \cap M)$$

If $$A = \{5, 7\}, B= \{7, 9\}$$ and $$C = \{7, 9, 11\},$$ find $$A \times (B \cup C)$$

If $$A = \{5, 7\}, B= \{7, 9\}$$ and $$C = \{7, 9, 11\},$$ find $$(A \times B) \cup (A \times C)$$

If $$n(A) = 4$$ and $$n(B) = 5$$, then $$n(A \times  B) = $$

If $$\displaystyle A=\left \{ 2, 3, 5 \right \}, B=\left \{ 2, 5, 6 \right \}$$ then  $$\left ( A-B \right )\times \left ( A\cap B \right )$$ is

If $$R$$ be a relation defined from $$\displaystyle A=\left \{ 1,2,3,4 \right \}$$ to $$\displaystyle B=\left \{ 1,3,5 \right \},i.e.\left ( a,b \right )\in R$$ iff $$a<b$$ then $$\displaystyle R o R^{-1}$$ is