Recent questions tagged mathematical-logic

Which of the following is/are logically equivalent to $\neg(P \Longrightarrow Q)?$$\neg P \vee Q$$\neg P \wedge Q$$Q \Longrightarrow P$$P \wedge \neg Q$

Which of the following best expresses the statement "Nobody loves everybody" in predicate logic?$\neg \exists x \forall y L(x, y)$$\neg \forall x \exists y L(x, y)$$\fora...

Which of the following represents the statement "There is exactly one person whom everybody loves"?$\exists x \forall y L(y, x)$$\exists x[\forall y L(y, x) \wedge \foral...

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

Let $\mathbf{T}(\mathbf{x}, \mathbf{y})$ be the predicate " $\mathbf{x}$ is taller than $\mathbf{y}$ ", where $\mathbf{x}, \mathbf{y} \in$ People. Consider the logical ex...

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 $1+1=3$