Given below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If a rectangle is a square,then all its four sides are equal.
$q:$ If all the four sides of a rectangle are equal,then the rectangle is a square.

Which of the following statements is/are False?
$S_1: \exists n \in N, \text{ such that } n^2 + n + 2 \text{ is divisible by 4.}$
$S_2: \exists x \in N, \text{ such that } x - 17 < 20.$
$S_3: \forall n \in N, x^2 + 3x - 10 = 0.$
$S_4: \forall n \in N, n^2 \ge 1.$

The statements $p, q$ and $r$ have truth values True, False and False respectively. The truth values of a logical statement $[\sim (p \land \sim q) \lor (q \lor \sim r)]$ and its dual are, respectively.....

Which of the following is false?

The contrapositive of the statement "If you are born in India,then you are a citizen of India" is:

$p \Rightarrow q$ can also be written as