The proposition p - p - q isA- A tautologyB- A contradictionC- Logically equivalent to p - qD- Niether tautology nor contradiction

Name: JEE- Grade 11- Mathematics- Mathematical Reasoning- Session 03- W17
Uploaded: 2022-07-04T10:36:42+05:30
Description: The correct option is A A tautology nbsp;[ p amp; q amp;∼ p amp; nbsp;∼ p nbsp; q amp; p ...

The correct option is A A tautology nbsp;[ p amp; q amp;∼ p amp; nbsp;∼ p nbsp; q amp; p ...

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Standard XII

Mathematics

Tautology

The propositi...

Question

The proposition $p \lor (\sim p \lor q)$ is

A tautology

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A contradiction

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Logically equivalent to

p \land q

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Niether tautology nor contradiction

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Solution

The correct option is A A tautology
$\begin{matrix} p & q & \sim p & \sim p \lor q & p \lor (\sim p \lor q) T & T & F & T & T T & F & F & F & T F & T & T & T & T F & F & T & T & T \end{matrix}$
Since the truth value of the given proposition is always true, it is a tautology.

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Similar questions

Q. The statement

p \land (\sim q \lor r) \lor (\sim r \lor q)

Q. The proposition

(p \Rightarrow\sim p) \land (\sim p \Rightarrow p)

is :

(p \land \sim q) \land (\sim p \land q)

Q. The statement

[(p \Rightarrow q) \land (q \Rightarrow r)] \Rightarrow (p \Rightarrow r)

Q. The logical statement

[(p \land q) \to p] \to (q \land \sim q)

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Tautology

Standard XII Mathematics

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The proposition p∨(∼p∨q) is

The correct option is A A tautology pq∼p∼p∨qp∨(∼p∨q)TTFTTTFFFTFTTTTFFTTT Since the truth value of the given proposition is always true, it is a tautology.

The proposition $p \lor (\sim p \lor q)$ is

The correct option is A A tautology
$\begin{matrix} p & q & \sim p & \sim p \lor q & p \lor (\sim p \lor q) T & T & F & T & T T & F & F & F & T F & T & T & T & T F & F & T & T & T \end{matrix}$
Since the truth value of the given proposition is always true, it is a tautology.