Find the component statements of the following compound statement:
All rational numbers are real and all real numbers are complex.

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.

The contrapositive of the statement,"If the side of a square doubles,then its area increases four times",is

The statement pattern $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to

The contrapositive of the statement,"If two lines do not intersect in the same plane,then they are parallel," is: