State which of the following sets are finite or infinite:
$A = \{ x : x \in \mathbb{N} \text{ and } x \text{ is prime} \}$

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $A \not\subset B$ and $B \not\subset C$,then $A \not\subset C$.

The set $A = \{ x : x \ne x \}$ represents:

Let $P$ and $T$ be the subsets of the $xy$-plane defined by $P = \{(x, y) : x > 0, y > 0 \text{ and } x^2 + y^2 = 1\}$ and $T = \{(x, y) : x > 0, y > 0 \text{ and } x^8 + y^8 < 1\}$. Then,$P \cap T$ is

If $Q = \{x : x = \frac{1}{y}, y \in N\}$,then which of the following is true?

If $X = \{a, b, c, d\}$ and $Y = \{f, b, d, g\},$ find $X - Y$.