Among the statements:(S1): (p Rightarrow q) v | vedclass

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

Question

(A) To determine if the statements are true,we construct truth tables for each.For $(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$| $p$ | $q$ | $p

Vedclass · Accepted Answer

neither $(S1)$ nor $(S2)$ is True

Vedclass · Answer

(A) To determine if the statements are true,we construct truth tables for each.For $(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$| $p$ | $q$ | $p \Rightarrow q$ | $\sim p \wedge q$ | $(p \Rightarrow q) \vee (\sim p \wedge q)$ ||---|---|---|---|---|| $T$ | $T$ | $T$ | $F$ | $T$ || $T$ | $F$ | $F$ | $F$ | $F$ || $F$ | $T$ | $T$ | $T$ | $T$ || $F$ | $F$ | $T$ | $F$ | $T$ |Since the last column contains an $F$,$(S1)$ is not a tautology. Thus,$(S1)$ is False.For $(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$| $p$ | $q$ | $q \Rightarrow p$ | $\sim p \wedge q$ | $(q \Rightarrow p) \Rightarrow (\sim p \wedge q)$ ||---|---|---|---|---|| $T$ | $T$ | $T$ | $F$ | $F$ || $T$ | $F$ | $T$ | $F$ | $F$ || $F$ | $T$ | $F$ | $T$ | $T$ || $F$ | $F$ | $T$ | $F$ | $F$ |Since the last column contains both $T$ and $F$,$(S2)$ is neither a tautology nor a contradiction. Thus,$(S2)$ is False.Therefore,neither $(S1)$ nor $(S2)$ is True.

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

Similar Questions

The number of switches in the alternative equivalent simple circuit for the given circuit is:

The minimum number of switches in the simplified form of the following switching circuit is

The statement $(p \wedge q) \to (p \vee q)$ is

The logical statement $[\sim(\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to

The following statement $(p \to q) \to [(\sim p \to q) \to q]$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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