Relations Test ...

 $$(x, y)$$ and $$(p, q)$$ are two ordered pairs. Find the values of $$p$$ and $$y$$, if $$(4y + 5, 3p - 1) = (25, p + 1)$$

$$(x, y)$$ and $$(p, q)$$ are two ordered pairs. Find the values of $$x$$ and $$p$$, if $$(3x - 1, 9) = (11, p + 2)$$

If $$A \times B = \{(3, a), (3, -1), (3, 0), (5, a), (5, -1), (5, 0)\}$$, find $$A$$.

If $$A = \{2, 3\}$$ and $$B = \{1, 2\}$$, find $$A \times B$$.

If $$A \times B =$$ $${(2, 4), (2, a), (2, 5), (1, 4), (1, a), (1, 5)}$$, find $$B$$.

Let $$A = \left \{1, 2, 3\right \}$$. Then number of relations containing $$(1, 2)$$ and $$(1, 3)$$ which are reflexive and symmetric but not transitive is

What is the relation for the following diagram?

Which of the following do(es) not belong to $$A \times B$$ for the sets $$A = \{1, 2\}$$ and $$B =\{0, 2\}$$?

Let $$S=\{(a, b, c) \in N \times N\times N:a+b+c=21, a \le b \le c\}$$ and $$T=\{(a, b, c)\in N\times N\times N: a, b, c\, are\, in\,AP\}$$, where $$N$$ is the set of all natural numbers. Then, the number of elements in the set $$S\cap T$$ is