If $n(X)=700, n(A)=200, n(B)=300,$ and $n(A \cap B)=100$,where $X$ is the universal set and $A$ and $B$ are subsets of $X$,then $n(A' \cap B')=$

Let $S$ be the set of all triangles in the $xy$-plane,each having one vertex at the origin and the other two vertices lying on the coordinate axes with integral coordinates. If each triangle in $S$ has an area of $50$ sq. units,then the number of elements in the set $S$ is:

In a class of $100$ students,$55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is

Two dice are thrown. The events $A$,$B$,and $C$ are as follows:
$A$: getting an even number on the first die.
$B$: getting an odd number on the first die.
$C$: getting the sum of the numbers on the dice $\leq 5$.
State whether the following statement is true or false and provide a reason:
Statement: $A$ and $C$ are mutually exclusive.

In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

If a set $A$ is such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$,then the set $A$ could be: