Relations Questions

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 $A=\{1,2,3,4,5\}$ and let $\ast$ is an operation on $A$ such that $a\ast b=\min \{a,b\}$. Which of the following is true?

Let $S=\{(x,y):x^2+y^2=1,-1\le x\in \mathbb{R}\le 1\text{ and }-1\le y\in \mathbb{R}\le 1\}$. Which one of the following is correct?

Let $R=\{(a,b):a,b\in \mathbb{N}\text{ and }{a}^2=b\}$. Which property does the relation $R$ satisfy?

Let $S$ denote all integers. Define a relation $R$ on $S$ as $aRb$ if $ab\ge 0$ where $a,b\in S$. Then $R$ is:

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

Let $m\in \mathbb{Z}$ and consider the relation $R_m$ defined by $a{R}_{m}b$ if and only if $a\equiv b(\mathrm{mod}m)$. Then $R_m$ 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: