Sets Questions

Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R=\{(x,y)\in W\times W\mid \text{the words }x\text{ and }y\text{ have at least one letter in common}\}$. Then $R$ is:

The set $S=\{1,2,3,\dots ,12\}$ is to be partitioned into three sets $A,B,C$ of equal size. Thus, $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$. The number of ways to partition $S$ is:

A die is thrown. Let $A$ be the event that the number obtained is greater than $3$. Let $B$ be the event that the number obtained is less than $5$. Then $P(A\cup B)$ is:

If $A,B$ and $C$ are three sets such that $A\cap B=A\cap C$ and $A\cup B=A\cup C$, then:

Let $\mathbb{R}$ be the set of real numbers.Statement-1 : $A=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x-y\text{ is an integer}\}$ is an equivalence relation on $\mathbb{R}$.Statement-2 : $B=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x=\alpha y\text{ for some rational number }\alpha \}$ is an equivalence relation on $\mathbb{R}$.

Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is:

Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}.$ The relation $R$ is