The solution set of $x \equiv 3 \pmod{7}$,where $p \in \mathbb{Z}$,is given by:

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 $A \subset B$ and $B \in C,$ then $A \in C$.

If $A = \{1, 2, 3, 4, 5\}$,then the number of proper subsets of $A$ is

Are the following pair of sets equal? Give reasons.
$A = \{ x : x \text{ is a letter in the word } \text{FOLLOW} \}$
$B = \{ y : y \text{ is a letter in the word } \text{WOLF} \}$

If $A = \{1, 2, 3, 4, 5, 6\}$, then which of the following is not true (in $in A$)?

If $aN = \{ax : x \in N\}$ and $bN \cap cN = dN$,where $b, c \in N$ are coprime numbers,then: