The statement (p wedge (p rightarrow q) wedge | vedclass

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

Question

(A) Let the statement be $S = (p \wedge (p$ $\rightarrow q) \wedge (q$ $\rightarrow r))$ $\rightarrow r$. Using the implication law $a \rightarrow b \

Vedclass · Accepted Answer

a tautology

Vedclass · Answer

(A) Let the statement be $S = (p \wedge (p$ $\rightarrow q) \wedge (q$ $\rightarrow r))$ $\rightarrow r$. Using the implication law $a \rightarrow b \equiv \sim a \vee b$,we have: $S \equiv \sim (p \wedge (p$ $\rightarrow q) \wedge (q$ $\rightarrow r)) \vee r$ Using De Morgan's law $\sim (A \wedge B \wedge C) \equiv \sim A \vee \sim B \vee \sim C$: $S \equiv \sim p \vee \sim (p$ $\rightarrow q) \vee \sim (q$ $\rightarrow r) \vee r$ Since $\sim (a \rightarrow b) \equiv a \wedge \sim b$: $S \equiv \sim p \vee (p \wedge \sim q) \vee (q \wedge \sim r) \vee r$ Using distributive law $\sim p \vee (p \wedge \sim q) \equiv (\sim p \vee p) \wedge (\sim p \vee \sim q) \equiv T \wedge (\sim p \vee \sim q) \equiv \sim p \vee \sim q$: $S \equiv (\sim p \vee \sim q) \vee (q \wedge \sim r) \vee r$ Using associative and distributive laws: $S \equiv \sim p \vee \sim q \vee (q \vee r) \wedge (\sim r \vee r)$ $S \equiv \sim p \vee \sim q \vee (q \vee r) \wedge T$ $S \equiv \sim p \vee (\sim q \vee q) \vee r$ $S \equiv \sim p \vee T \vee r \equiv T$ Since the result is always true,the statement is a tautology.

The statement $(p \wedge (p$ $\rightarrow q) \wedge (q$ $\rightarrow r))$ $\rightarrow r$ is :

Similar Questions

Which of the following is not a statement?

Let,$p$: Ramesh listens to music.
$q$: Ramesh is out of his village.
$r$: It is Sunday.
$s$: It is Saturday.
Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as:

Consider
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.

For the circuit shown below,the Boolean polynomial is

If the truth value of $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is false, then which of the following is $NOT$ true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module