The logical statement 

[\sim(\sim p\vee q)\vee (p\wedge r)]\wedge (\sim q \wedge r)

is equivalent to :

  • Option 1)

     

    (\sim p \wedge \sim q)\wedge r

  • Option 2)

     

    (p\wedge \sim q) \vee r

  • Option 3)

     

    \sim p \vee r

  • Option 4)

     

    (p \wedge r) \wedge \sim q

Answers (1)
A admin

 

Truth value of "And" Conjuction -

The statement p\wedge q has the truth value T whenever both p and q have the truth value T.

-

 

 

Truth Value of Disjunction "OR" -

The statement p\veeq has the truth value F if both p and q have the truth value F.

-

 

 

Negation of a Statement -

Negation is a connective although it doesn't combine two or more statements

-

 

Given,

[\sim (\sim p\vee q)\vee (p\wedge r) \wedge (\sim q\wedge r))] \\ = [ (p\wedge \sim q)\vee (p\wedge r)] \wedge (\sim q\wedge r)) \\ = [ (p\wedge (\sim q\vee r)] \wedge (\sim q\wedge r)) \\= p\wedge (\sim q\wedge r) \\ \equiv (p\wedge r)\wedge \sim q


Option 1)

 

(\sim p \wedge \sim q)\wedge r

Option 2)

 

(p\wedge \sim q) \vee r

Option 3)

 

\sim p \vee r

Option 4)

 

(p \wedge r) \wedge \sim q

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