Consider :

Statement - I : (p\, \wedge \sim q)\; \wedge \; (\sim p\wedge q)\; is \; a fallacy

Statement - II : (p\, \rightarrow q)\; \leftrightarrow \; (\sim q\, \rightarrow \; \sim p)\; is \; a\; tautology.

 

 

 

  • Option 1)

    Statement - I is false ; Statement - II is true.

     

  • Option 2)

    Statement - I is true ; Statement - II is true ; Statement - II is a correct explanation for Statement - I.

     

     

  • Option 3)

    Statement - I is true ; Statement - II is true ; Statement - II is not a correct explanation for Statement - I.

     

     

  • Option 4)

    Statement - I is true ; Statement - II is false.

     

     

 

Answers (1)

As learnt in

Truth Table of 'AND' operator -

Figure 1

-

 

 

Truth table of 'OR' operator -

-

 

 

Truth Table of "if-then" -

Figure 4

-

 

 

Truth Table of "if and only if" -

Figure 5

-

 

 

Tautology -

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

-

 

 

Fallacy or contradiction -

A statement pattern is called a fallacy if it is always false, whatever may be the truth values of its constituent statements.

-

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

It is fallacy.

p
q
p\rightarrow q
\sim q\rightarrow \sim p
\left ( p\rightarrow q \right )\leftrightarrow \left ( \sim q\rightarrow \sim p \right )
T
T
T
T
T
T
F
F
F
T
F
T
T
T
T
F
F
T
T
T

It is tautology


Option 1)

Statement - I is false ; Statement - II is true.

 

Incorrect option

Option 2)

Statement - I is true ; Statement - II is true ; Statement - II is a correct explanation for Statement - I.

 

 

Incorrect option

Option 3)

Statement - I is true ; Statement - II is true ; Statement - II is not a correct explanation for Statement - I.

 

 

Correct option

Option 4)

Statement - I is true ; Statement - II is false.

 

 

Incorrect option

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