What is the identity element for the conjunction $(AND)$ operation in Boolean algebra of logical statements?

Are the following pairs of statements negations of each other:
$1$. The number $x$ is a rational number.
$2$. The number $x$ is an irrational number.

Consider the following three statements:
$(A)$ If $3+2=7$ then $4+3=8$.
$(B)$ If $5+2=7$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=11$.
Which of the following statements is correct?

The statement pattern $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to

Given the statement: "If you live in Delhi,then you have winter clothes."
Identify the following statements as contrapositive or converse of the given statement:
$(i)$ If you do not have winter clothes,then you do not live in Delhi.
$(ii)$ If you have winter clothes,then you live in Delhi.

Find the component statements of the following and check whether they are true or not.
$\sqrt{2}$ is a rational number or an irrational number.