implication

'When the teacher is in the room, all students stand silently.' If the above statement is true, which one of the following statements is not necessarily true?

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

Let $P(x)$ be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?

Let p and q be the following propositions: p : Fail grade can be given. q : Student scores more than 50% marks. Consider the statement: “Fail grade cannot be given when student sco...

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. $...

Which one of the following well formed formulae is a tautology?

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...

Which of the following is the negation of $$$\left[ {\forall x,\alpha \to \left( {\exists y,\beta \to \left( {\forall u,\exists v,\gamma } \right)} \right)} \right]?$$$

Which of the following first order formulae is logically valid? Here $$\alpha \left( x \right)$$ is a first order formulae with $$x$$ as a free variable, and $$\beta $$ is a first...

Let $$P, Q$$ and $$R$$ be three atomic prepositional assertions. Let $$X$$ denotes $$\left( {P \vee Q} \right) \to R$$ and $$Y$$ denote $$\left( {P \to R} \right) \vee \left( {Q \t...

"If X then Y unless Z" is represented by which of the following formulas in propositional logic? (" $$\neg $$ " is negation, " $$ \wedge $$ " is conjunction, and " $$ \to $$ " is i...

What is the converse of the following assertion? I stay only if you go

Which of the following is/are tautology?