The logically equivalent statement of $(\sim p \wedge q) \vee (\sim p \wedge \sim q) \vee (p \wedge \sim q)$ is

Simplify $(p \vee q) \wedge (p \vee \sim q)$

Show that the following statement is true by the method of contrapositive.
$p:$ If $x$ is an integer and $x^{2}$ is even,then $x$ is also even.

Which of the following statements is a tautology?

Identify the type of "Or" used in the following statement and check whether the statement is true or false:
To enter into a public library,children need an identity card from the school or a letter from the school authorities.

If the Boolean expression $(p \oplus q) \wedge (\sim p \Theta q)$ is equivalent to $p \wedge q$,where $\oplus, \Theta \in \{\wedge, \vee\}$,then the ordered pair $(\oplus, \Theta)$ is: