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The following statement

\left ( p\rightarrow q\right )\rightarrow \left [ \left ( \sim p\rightarrow q \right ) \rightarrow q\right ] is

  • Option 1)

    equivalent to \sim p\rightarrow q

  • Option 2)

    equivalent to p\rightarrow \sim q

  • Option 3)

    a fallacy

  • Option 4)

     a tautology

 

Answers (1)

As we learnt in 

Truth Table of "if-then" -

Figure 4

-

 

   

Truth Table of "if-then" -

Figure 4

-

 

 

Tautology -

 

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

-

 

 Statement is \left ( p\rightarrow q \right )\rightarrow \left [ \left ( \sim p\rightarrow q \right ) \rightarrow q\right ]

 

                Truth Value                                                                                                     (Statement to prove)

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

It is always True.

So its a tantology.


Option 1)

equivalent to \sim p\rightarrow q

Incorrect

Option 2)

equivalent to p\rightarrow \sim q

Incorrect

Option 3)

a fallacy

Incorrect

Option 4)

 a tautology

Correct

Posted by

Vakul

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