A Class-Room Introduction to Logic

May 4, 2009

Unit-XVII: Validity and Invalidity by Truth-table Method

Filed under: Validity through Truth table — Dr. Desh Raj Sirswal @ 5:57 am

We can determine the validity of compound statement by Truth-table method in two forms.

NOTE : É  represents implication and /\ represents disjunction and Ú represents conjunction.

I. REPLACES THE TERMS BY GIVEN VALUES:

If  A and B are true statements and X and Y are false statement , find out whether compound statements are true .For example:

(AÉ B) · ( X É Y )

Solution:            (AÉ B) · ( X É Y )

(TÉ T) · ( F É F)

T      ·      T

T                   Ans.

Another Examples:

1.         X É ( X É Y )

2.         (X É X ) É Y

3.         A É ( X É B )

4.         (A É B) É (~A É ~B )

 

II.        Determine the validity and invalidity of the following Compound statements: In deductive logic, it is assumed that if the premises are true the conclusion must be true. In this we will draw truth-table and by this we can determine the validity and invalidity of the given statements. And also give justification for this. For Example:   pÉq /\ q

Solution:         pÉq/\ q

Statement     Conclusion

p

q

p É q

q

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

Ans. Invalid, because in the fourth row the table conclusion is the false although the premise is true.

For example:            

1.         p É q /\ ~q É ~p

2.         p É q

q /\ q

3.         If Mohan goes to Meerut, then Sohan goes to Delhi. Sohan goes to Delhi. Therefore, Mohan goes to Meerut.

 

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