Sets Questions

In throwing a six-faced die, let A be the event that an even number occurs, B be the event that an odd number occurs, and C be the event that a number greater than 3 occurs. Which one of the following is correct?

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?

A card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is either an Ace or a King?

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:

If $n(U)=1000$, $n(X)=300$, $n(Y)=400$ and $n(X\cap Y)=200$, then find $n(P(X^{\prime }\cap Y^{\prime }))$.