logic

'When it is raining, peacocks dance.' Based only on this sentence, which one of the following options is necessarily true?

Consider the relationships among $P, Q, R, S$, and $T$ : $\bullet$ $P$ is the brother of $Q$. $\bullet$ $S$ is the daughter of $Q$. $\bullet$ $T$ is the sister of $S$. $\bullet$ $R...

Given below are two statements I and II and two conclusions I and II : Statement : I. All bacteria are microorganisms. II. All pathogens are microorganisms. Conclusions : I. Some p...

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her...

The statement $(\neg p) \Rightarrow(\neg q)$ is logically equivalent to which of the statements below? I. $\quad p \Rightarrow q$ II. $q \Rightarrow p$ III. $(\neg q) \vee p$ IV. $...

Consider the following two statements. $$S1:$$ If a candidate is known to be corrupt, then he will not be elected $$S2:$$ If a candidate is kind, he will be elected Which one of th...

Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which of the follow...

Consider the following logical inferences. $${{\rm I}_1}:$$ If it rains then the cricket match will not be played. The cricket match was played. Inference: there was no rain. $${{\...

The following resolution rule is used in logic programming. Derive clause $$\left( {P \vee Q} \right)$$ from clauses $$\left( {P \vee R} \right)$$, $$\left( {Q \vee \neg R} \right)...

Which one of the following is false? Read $$ \wedge $$ as AND, $$ \vee $$ as OR, $$ \sim $$ as NOT, $$ \to $$ as one way implication and $$ \leftrightarrow $$ two way implication.