Relations Test ...

If $$p - q > 0$$, which of the following is true?

Let $$R$$ be a relation defined on the set $$Z$$ of all integers and $$xRy$$ when $$x + 2y$$ is divisible by $$3$$. Then

The relation R define on the set of natural numbers as {(a, b) : a differs from b by 3} is given.

The relation 'has the same father as' over the set of children is:

If A and B are two non-empty sets having n elements in common, then what is the number of common elements in the sets $$A\times B$$ and $$B\times A$$?

Let $$A=\left\{ x\in W,the\quad set\quad of\quad whole\quad numbers\quad and\quad x<3 \right\} $$

Let $$A = \left\{ a,b,c,d \right\}$$ and $$ B=\left\{ x,y,z \right\}$$. What is the number of elements in $$ A\times B$$?

If $$A = \left\{ 1,2 \right\}$$, $$B = \left\{ 2,3 \right\}$$ and $$ C = \left\{ 3,4 \right\}$$, then what is the cardinality of $$ \left( A\times B \right) \cap \left( A\times C \right) $$

A and B are two sets having $$3$$ elements in common. If $$n(A)=5, n(B)=4$$, then what is $$n(A\times B)$$ equal to?

Let $$Z$$ be the set of integers and $$aRb$$, where $$a, b\epsilon Z$$ if an only if $$(a - b)$$ is divisible by $$5$$.
Consider the following statements:
$$1.$$ The relation $$R$$ partitions $$Z$$ into five equivalent classes.
$$2.$$ Any two equivalent classes are either equal or disjoint.
Which of the above statements is/are correct?