Which statement given below is a tautology?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) statement is a tautology if its truth value is always true for all possible truth values of its components.$(A)$ $p$ $\rightarrow (p \land (p$ $\r

Vedclass · Accepted Answer

$(p \land q)$ $\rightarrow (\sim p$ $\rightarrow q)$

Vedclass · Answer

(B) statement is a tautology if its truth value is always true for all possible truth values of its components.$(A)$ $p$ $\rightarrow (p \land (p$ $\rightarrow q)) \equiv \sim p \lor (p \land (\sim p \lor q)) \equiv \sim p \lor ((p \land \sim p) \lor (p \land q)) \equiv \sim p \lor (F \lor (p \land q)) \equiv \sim p \lor p \land q \equiv (\sim p \lor p) \land (\sim p \lor q) \equiv T \land (\sim p \lor q) \equiv \sim p \lor q$. This is not a tautology.$(B)$ $(p \land q)$ $\rightarrow (\sim p$ $\rightarrow q) \equiv \sim(p \land q) \lor (\sim(\sim p) \lor q) \equiv (\sim p \lor \sim q) \lor (p \lor q) \equiv (\sim p \lor p) \lor (\sim q \lor q) \equiv T \lor T \equiv T$. This is a tautology.$(C)$ $(p \land (p$ $\rightarrow q))$ $\rightarrow \sim q \equiv \sim(p \land (\sim p \lor q)) \lor \sim q \equiv \sim((p \land \sim p) \lor (p \land q)) \lor \sim q \equiv \sim(F \lor (p \land q)) \lor \sim q \equiv \sim(p \land q) \lor \sim q \equiv \sim p \lor \sim q \lor \sim q \equiv \sim p \lor \sim q$. This is not a tautology.$(D)$ $p \lor (p \land q) \equiv p$. This is not a tautology.

Similar Questions

The statement $[(p \wedge q)$ $\rightarrow p]$ $\rightarrow (q \wedge \sim q)$ is

Which of the following statements is a tautology?

If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

If the statement $p \leftrightarrow (q \rightarrow p)$ is false,then the true statement/statement pattern is

Which of the following statement patterns is a tautology?
$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$
$S_{2} \equiv \sim p \vee \sim q$
$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$
$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module