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Maths NCERT Exemplar Solutions Class 11th Chapter Two Mathematical Reasoning Ncert Solutions Maths class 11th Maths Class 11th

Consider the following two propositions:

$P 1 : \sim (p \to \sim q)$

$P 2 : (p \land \sim q) \land ((\sim p) \lor q)$

If the proposition p ® $((\sim p) \lor q)$ is evaluated as FALSE, then :

Option 1 -

P1 is TRUE and P2 is FALSE

Option 2 -

P1 is FALSE and P2 is TRUE

Option 3 -

Both P1 and P2 are FALSE

Option 4 -

Both P1 and P2 are TRUE

4 Views | Posted 3 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

3 weeks ago

Correct Option - 4

Detailed Solution:

$p_{1} : \sim (p \leftrightarrow \sim q)$ $p_{2} : (p \land \sim q) \land ((\sim p) \lor q)$

$= \sim ((\sim p) \lor (\sim q))$

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

$p \land q$

$(\sim p) \lor ((\sim p) \lor q)$ is false (given)

p q p₁ p₂ $(\sim p) \lor q$

T F T

...more

$p_{1} : \sim (p \leftrightarrow \sim q)$ $p_{2} : (p \land \sim q) \land ((\sim p) \lor q)$

$= \sim ((\sim p) \lor (\sim q))$

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

$p \land q$

$(\sim p) \lor ((\sim p) \lor q)$ is false (given)

p q p₁ p₂ $(\sim p) \lor q$

T F T

T F F

F T F T

F T

less

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Consider the following two propositions:

$P 1 : \sim (p \to \sim q)$

$P 2 : (p \land \sim q) \land ((\sim p) \lor q)$

If the proposition p ® $((\sim p) \lor q)$ is evaluated as FALSE, then :

1 Answer

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Consider the following two propositions: P 1 : ∼ ( p → ∼ q ) P 2 : ( p ∧ ∼ q ) ∧ ( ( ∼ p ) ∨ q ) If the proposition p ® ( ( ∼ p ) ∨ q ) is evaluated as FALSE, then :

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Consider the following two propositions:

$P 1 : \sim (p \to \sim q)$

$P 2 : (p \land \sim q) \land ((\sim p) \lor q)$

If the proposition p ® $((\sim p) \lor q)$ is evaluated as FALSE, then :