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
pÚ q /\ q
3. If Mohan goes to Meerut, then Sohan goes to Delhi. Sohan goes to Delhi. Therefore, Mohan goes to Meerut.