Let r in {p, q, sim p, sim q} be such that th | vedclass

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

Question

(C) To determine which $r$ makes the statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ a tautology,we test each option using a truth table.F

Vedclass · Accepted Answer

$\sim p$

Vedclass · Answer

(C) To determine which $r$ makes the statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ a tautology,we test each option using a truth table.For $r = \sim p$:The statement becomes $(\sim p \vee \sim p) \Rightarrow (p \wedge q) \vee \sim p$.This simplifies to $\sim p \Rightarrow (p \wedge q) \vee \sim p$.Using the law of absorption,$(p \wedge q) \vee \sim p$ is equivalent to $(\sim p \vee p) \wedge (\sim p \vee q)$,which is $T \wedge (\sim p \vee q) = \sim p \vee q$.So the statement is $\sim p \Rightarrow (\sim p \vee q)$.Since $\sim p \Rightarrow (\sim p \vee q)$ is equivalent to $
eg(\sim p) \vee (\sim p \vee q) = p \vee \sim p \vee q = T \vee q = T$,the statement is a tautology.Thus,$r = \sim p$ is the correct option.

Let $r \in \{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ is a tautology. Then $r$ is equal to

Similar Questions

Check whether the following sentence is a statement. Give reasons for your answer.
Mathematics is fun.

Consider the following statements:
$P :$ Ramu is intelligent
$Q :$ Ramu is rich
$R :$ Ramu is not honest
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

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

If $A$: Lotuses are Pink and $B$: The Earth is a planet. Then the verbal translation of $(\sim A) \vee B$ is

Write the following statement in five different ways,conveying the same meaning.
$p:$ If a triangle is equiangular,then it is an obtuse-angled triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module