Set Theory Questions

Which of the following is an empty set?

Let $X$ be the set of all persons living in a city. Persons $x,y\in X$ are said to be related as $x<y$ if $y$ is at least $5$ years older than $x$. Which one of the following is correct?

If $\ast$ is a binary operation on $A=\{1,2,3,4,5\}$ defined by the table below:∗12345111111212121311311412141511115Find the value of $(3\ast 3)\ast (4\ast 4)$.

Let $R$ be the relation on the set $\mathbb{R}$ of all real numbers defined by $aRb$ if $|a-b|\le 1$. Then $R$ is:

If $a\mathbb{N}=\{ax:x\in \mathbb{N}\}$, then $2\mathbb{N}\cap 5\mathbb{N}$ is:

A coin is tossed twice. If $E$ and $F$ denote the occurrence of a head on the first toss and second toss respectively, then what is $P(E\cup F)$ equal to?

In a survey of $100$ people, $60$ like tea, $50$ like coffee, and $25$ like both tea and coffee. How many people like neither tea nor coffee?

Let $R$ be a relation on the set of natural numbers defined by $xRy⟺x\le y$. Which one of the following is correct?

The identity element for the binary operation $\ast$ defined on $\mathbb{Q}-\{0\}$ as $a\ast b=\frac{ab}{2}$ is:

If $A=\{1,2,3\}$ and $R$ is a relation defined on $A$ such that $R=\{(1,1),(1,2),(2,3),(2,2),(3,3),(3,1)\}$. Then the relation $R$ is: