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In this post,Let us understand Tautology, Contradiction, and Contingency
In Propositional logic, every statement falls into one of the types using truth table
- Tautology
- Contradiction
- Contingency
I hope,you know the Propositional logic.if you don't know, Please click the Propositional logic link in discrete mathematics menu and learn the Propositional logic in my blog.
Now, Let us come to the concepts of Tautology, Contradictions, Contingency.
Tautology:
A Tautology is a statement that is always true values.
For example:
Truth table
p ¬p p ∨ ¬p
T F T
F T T
Explanation:
Tautology means the truth table of the last column is always true.
Look at the above example,First column is T, F, Second column is F,T ,and to compute the third column of p or not p is true.This is called tautology.
Contradiction:
A Contradiction is a statement that is always false values.
For example:
p ¬p p ∧ ¬p
T F F
F T F
Explanation:
Contradiction means the truth table of the last column is always false.
Look at the above example,the truth table of first column is p ,T,F , Second column is not p ,T,F and now to compute the third column of p and not p is always false.This is called Contradiction.
Contingency:
A contingency is a statement,that is sometimes true and sometimes false.
For example:
Truth Table
p ¬p p → ¬p
T F F
F T T
Explanation:
Contingency means it is sometimes true and sometimes false
Look at the above example,the first column of p is T,F , Second column of not p is F,T and to compute the third column of p implies not p is F and T. This is called Contingency.
Conclusion:
I hope,this post helps you to understand the Tautology, Contradiction and Contingency.If you like this post, like and share this post with your friends,Please follow it for more updates.
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