Recent questions tagged propositional-logic

Negation of $p \wedge(q \wedge \sim(p \wedge q))$ is :$(\sim(p \wedge q)) \wedge q$ $(\sim(p \wedge q)) \vee p$ $p \vee q$ $\sim(p \vee q)$

The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is$A \vee B$ $C \vee D$ $A \vee C$ $A \vee D$

Let $P$ and $Q$ be two propositions $\neg(P \leftrightarrow Q)$ is equivalent to$P \leftrightarrow \neg Q$ $\neg P \leftrightarrow Q$ $\neg P \leftrightarrow \neg Q$ $Q \...

Statement $(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to :$(P \Rightarrow R) \wedge(Q \Rightarrow R)$ $(P \Rightarrow R) \vee(Q \Rightarrow R)$ $(...

Consider the formula:$$[(p \rightarrow q) \wedge(r \rightarrow \neg q)] \rightarrow(r \rightarrow \neg p)$$If the formula is a tautology, submit your answer as $\mathbf{1...

Consider the following logical sentences. For each sentence, comment on its validity and satisfiability:1. (Smoke $\rightarrow$ Fire $) \rightarrow(\neg$ Smoke $\rightarr...

Match List-I with List-II and choose the correct answer from the code given below :\[\begin{array}{|c|l|c|l|}\hline\text{} & \text{List I} & \text{} & \text{List II} \\\h...

The first order logic (FOL) statement $((R \vee Q) \wedge(P \vee \neg Q))$ is equivalent to which of the following?A. $((R \vee \neg Q) \wedge(P \vee \neg Q) \wedge(R \ve...

Which of the following expressions is a tautology?$(P \rightarrow Q) \vee(Q \rightarrow P)$ $(P \vee Q) \rightarrow(P \rightarrow Q)$ $((P \rightarrow Q) \wedge P) \right...

Statement: A sufficient condition for the warranty to be good is that you bought the computer less than a year ago.Let:P: You bought the computer less than a year ago.Q: ...

Statement: It is necessary to wash the boss's car to get promoted.Let:P: You wash the boss's car.Q: You get promoted.Which of the following propositional formulas express...

Let $\varphi$ be a propositional formula on $n$ variables, with $n \geq 1$. Consider the following statements.$\varphi$ is satisfiable$\neg \varphi$ is unsatisfiable$\var...

Three boxes are presented to you. One contains gold, the other two are empty. Each box has imprinted on it a clue as to its contents; the clues areI. (Box 1) The gold is ...

Determine if the following deduction rule is validp → q~q → ~r_________∴ p → r TrueFalse

Is $(\mathrm{p} \rightarrow \mathrm{q})^{\prime} \equiv \mathrm{p} \wedge \mathrm{q}^{\prime}$ ?TrueFalse

If a truth table has five proposition labels, how many rows of truth values will the complete truth table have?5163264

Which of the inferences are valid given the premises?$\begin{array}{l}\text{} (I_{1})\text{}\end{array} \quad \begin{array}{l}\text{All birds have feathers.} \\\text{Robi...

Consider the statement form $p \Rightarrow q$ where $p=$ "If Tom is Jane's father then Jane is Bill's niece" and $q=$ "Bill is Tom's brother." Which of the following stat...

Q4. The statement form $(p \Leftrightarrow r) \Rightarrow(q \Leftrightarrow r)$ is logically equivalent to:$(\sim p \vee r) \wedge(\sim r \vee p) \Rightarrow(\sim q \vee ...

Which of the following statements are tautologies?(You may select more than one option.)$(p \wedge q) \rightarrow p$$p \rightarrow(p \vee q)$$p \rightarrow(p \rightarrow ...

How many different truth tables of compound propositions are there that involve the propositional variables $p$ and $q$ ?

Mark all the statements that are logically true:If $1+1=2$, then $2+2=5$If $1+1=2$, then $2+2=4$If $1+1=3$, then $2+2=5$If monkeys can fly, then $1+1=3$