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  • Need explanation for: - If q is false and is true, then which one of the following statements is a tautology? - Mathematical reasoning - JEE Main

If q is false and p\wedge q\leftrightarrow r  is true, then which one of the following statements is a tautology?

 

  • Option 1)

     

    (p \vee r)\rightarrow (p\wedge r)

  • Option 2)

     

    p\wedge r

  • Option 3)

     

    p \vee r

  • Option 4)

     

    (p \wedge r)\rightarrow (p\vee r)

Answers (1)

best_answer

 

Tautology -

A statement pattern is called tautalogy, if it is always true, whatever may be the truth values of constitute statements.

-

 

 

Truth Table of 'AND' operator -

Figure 1

-

 

 

Truth Table of "if and only if" -

Figure 5

-

 

 

Truth table of 'OR' operator -

-

 

 

(p\wedge q)\leftrightarrow r is true

Case 1  p\wedge q is true and r is true It is not possible as q is false

Case 2    p\wedge q is false and r is false

\Rightarrow p\equiv T/F

r\equiv F

p\vee r\rightarrow p\wedge r\Rightarrow T or F \rightarrow F which may be T/F

p\wedge r\rightarrow p \vee r\Rightarrow F \rightarrow T/F which is always True. 


Option 1)

 

(p \vee r)\rightarrow (p\wedge r)

Option 2)

 

p\wedge r

Option 3)

 

p \vee r

Option 4)

 

(p \wedge r)\rightarrow (p\vee r)
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