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Can someone help me with this, - If the Boolean expressionis equivalent to, where, then the ordered pairis: - Mathematical reasoning - JEE Main

If the Boolean expression (p\oplus q) \wedge (\sim p \odot q) is equivalent to p \wedge q , where  \oplus, \odot \in \{ \wedge, \vee\}, then the ordered pair (\oplus, \odot) is:

  • Option 1)

    (\wedge, \vee)

  • Option 2)

    (\vee,\vee)

  • Option 3)

    (\vee, \wedge)

  • Option 4)

    (\wedge,\wedge)

Answers (1)
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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

-

Make truth table.

 

P q \sim p p\wedge q p\vee q \sim p\vee q \sim p\wedge q \left ( p\wedge q \right )\wedge\left ( \sim p\vee q \right )
T    F T T

T

F T
T F F F T F F F
F T T F T T T F
F F T F F T F F

 

 


Option 1)

(\wedge, \vee)

Option 2)

(\vee,\vee)

Option 3)

(\vee, \wedge)

Option 4)

(\wedge,\wedge)

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