If $(x+1, y-2) = (3, 1)$,find the values of $x$ and $y$.

The Cartesian product $A \times A$ has $9$ elements,among which are found $(-1, 0)$ and $(0, 1)$. Find the set $A$ and the remaining elements of $A \times A$.

Let $A = \{a, b, c\}$ and $B = \{1, 2\}$. Then the relation $R$ defined from set $A$ to set $B$ is a subset of which of the following?

If the set $A$ has $3$ elements and the set $B = \{3, 4, 5\},$ then find the number of elements in $(A \times B).$

State whether the following statement is true or false. If the statement is false,rewrite it correctly.
If $A = \{1, 2\}$ and $B = \{3, 4\}$,then $A \times \{B \cap \varnothing\} = \varnothing$.

If $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are