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

If $A$: Lotuses are Pink and $B$: The Earth is a planet. Then the verbal translation of $(\sim A) \vee B$ is

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?

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 direct method.

Check whether the following sentence is a statement. Give reasons for your answer.
There is no rain without clouds.

The statements $p, q$ and $r$ have truth values $T, F$ and $F$ respectively. The truth values of a logical statement $[\sim (p \wedge \sim q) \vee (q \vee \sim r)]$ and its dual are, respectively.....