Recent questions tagged propositional-logic

Which of the followings logical implications are tautology?$[\sim p \wedge(p \vee q)] \rightarrow q$$\sim p \rightarrow(p \rightarrow q)$$[p \wedge(p \rightarrow q)] \rig...

Match the LIST-I with LIST-II LIST-I LIST-IIA.Definite clauseI.Forward ChainingB.Horn ClauseII.At most ine if postive literalsC.Goal ClauseIII.No positive literalsD.Infer...

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason RAssertion A: Validity can never apply to any single proposition by its...

For the statement $$P \rightarrow Q$$Which of the following statements below is/are correct?If the hypothesis is true and the conclusion is false, then the conditional st...

The compound statement $(\sim(P \wedge Q)) \vee((\sim P) \wedge Q) \Rightarrow((\sim P) \wedge(\sim Q))$ is equivalent to$((\sim P) \vee Q) \wedge(\sim Q)$$(\sim Q) \vee ...

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $(\mathrm{p} \rightarrow \mathrm{q}) \Delta(\mathrm{p} \nabla \mathrm{q})$ is a tautology. Then$\Delta=\vee, \nabla=...

If $p, q$ and $r$ are three propositions, then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\si...

Consider the following statements:P : I have feverQ: I will not take medicineR : I will take rest.The statement "If I have fever, then I will take medicine and I will tak...

Among the two statements(S1) : $(p \Rightarrow q) \wedge(p \wedge(\sim q))$ is a contradiction and(S2) : $(p \wedge q) \vee((\sim p) \wedge q) \vee(p \wedge(\sim q)) \vee...

The negation of the statement $((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$ isequivalent to $B \vee \sim C$equivalent to $\sim A$equivalent to $\sim C$a fa...

The statement $(p \wedge(\sim q)) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$ is equivalent to $\_\_\_\_$ .$(\sim p) \vee(\sim q)$$p \vee(\sim q)$$p \vee q$$(\...

Let $p$ : "Jupiter is a planet" and $q$ : "India is an island." Which of the following is the correct verbal description of $p \rightarrow \neg q$ ?Jupiter is a planet if...

Let $p$ : "Jupiter is a planet" and $q$ : "India is an island." Which of the following is the correct verbal description of $\neg p$ ?Jupiter is a planet and India is an ...

Aunt Nellie baked a pie and left it to cool. Upon returning home she finds that exactly one of her four visiting relatives - Charles, Kelly, Dawn, or Tyler - has eaten a ...

Given the premises:$$H_1: \neg P \vee Q, \quad H_2: \neg(Q \wedge \neg R), \quad H_3: \neg R$$Which of the following conclusions is logically valid?$C: P$ $C: Q$ $C: \neg...

Given the premise $H_1: P \rightarrow Q$, which of the following conclusions $C$ is logically valid?$C:P \rightarrow (P \vee Q)$$C: P\rightarrow (P \wedge Q)$$C: Q\righta...

A government installation has an alarm system modelled as:$$A \Leftrightarrow M \wedge(D \vee(G \wedge \neg S))$$and a recording system modelled as:$$R \Leftrightarrow G ...

A government installation has an alarm system modelled as:$$A \Leftrightarrow M \wedge(D \vee(G \wedge \neg S))$$where $M=$ Master switch is ON, $D=$ Door is disturbed, $...

A government installation has the following two rules:- Alarm: $A \Leftrightarrow M \wedge(D \vee(G \wedge \neg S))$- Recording: $R \Leftrightarrow G \wedge (\neg M \wedg...

A government installation has an alarm system modelled as:$$A \Leftrightarrow M \wedge(D \vee(G \wedge \neg S))$$where $M=$ Master switch is $\mathrm{ON}, D=$ Door is dis...

A government installation requires an automatic recording instrument to log every entry into the restricted-access area under specific conditions. Recording happens when ...

A government installation has an intruder alarm system. The alarm sounds only when the master switch is ON. When ON, the alarm triggers if either the restricted access do...

How many rows of the truth table of $(P \vee Q) \wedge(\neg P \wedge(\neg P \wedge Q))$ evaluate to TRUE?

Which of the following is logically equivalent to $\neg(P \wedge Q) \rightarrow(\neg P \vee(\neg P \vee Q))$ ?$\neg P \wedge Q$ $\neg P \vee Q$ $P \wedge \neg Q$ $P \vee ...

Let $\mathrm{p}=$ "It is cold" and $\mathrm{q}=$ "It is raining." Which of the following is the correct verbal translation of $ q\vee \neg p$ ?It is not raining or it is ...

In classical propositional logic, which of the following correctly distinguishes inclusive OR (v) from exclusive OR ( $\oplus$ )?$p \vee q$ is TRUE when at least one of $...

For each of the following sentences, determine which involve an EXCLUSIVE OR (meaning one or the other but not both). Select all that apply.Experience with C++ or Java is...

Which of the following conditional statements is FALSE?If $1+1=3$, then unicorns exist.If $1+1=3$, then dogs can fly.If $1+1=2$, then dogs can fly.If $2+2=4$, then $1+2=3...

Determine which of the following conditional statements are TRUE. Select all that apply.If $1+1=2$, then $2+2=5$.If $1+1=3$, then $2+2=4$.If $1+1=3$, then $2+2=5$.If monk...