Which of the following Boolean expressions is a tautology?

The statement $(p$ $\rightarrow (q$ $\rightarrow p))$ $\rightarrow (p$ $\rightarrow (p \vee q))$ is

If $p$ : the function $f(x) = x$ is an even function,$q$ : ${}^nC_m$ is a whole number wherever defined,and $r$ : if $\overrightarrow{c} = \overrightarrow{a} + \lambda \overrightarrow{b}$,then the vectors $\overrightarrow{a}, \overrightarrow{b}$,and $\overrightarrow{c}$ are linearly dependent. Which one of the following statements is true?

Show that the statement $p:$ 'If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$' is true by the method of contradiction.

Find the component statements of the following and check whether they are true or not.
$A$ person who has taken Mathematics or Computer Science can go for $MCA$.

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