Examine whether the following statement is true or false:
${1, 2, 3} \subset {1, 3, 5}$

Which set is the subset of all given sets?

Let $A = \{a, e, i, o, u\}$ and $B = \{a, b, c, d\}$. Is $A$ a subset of $B$? No. (Why?). Is $B$ a subset of $A$? No. (Why?)

Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)

How many elements does $P(A)$ have,if $A = \varnothing$?

List all the elements of the following set:
$B = \{ x : x \text{ is an integer}; -\frac{1}{2} < x < \frac{9}{2} \}$