For a conditional statement p→q, we can write three related conditional statements as,
Converse: q → p
Contrapositive: ¬q → ¬p
Inverse: ¬p → ¬q
Only Contrapositive will have same truth values as p→q.
Tautology:- A compound statement which is always true is called a tautology.
Contradiction:- A compound statement which is always false is called a contradiction.
Contingency:- A compound statement which is neither a tautology nor a contradiction is called a contingency.
Logically equivalent:- The compound propostions p and q are called logically equivalent if p↔q is a tautology.
Satisfiability:-A formula is called satisfiable if it is true for atleast one case or interpretation.
Validity:- A formula is called valid if it is true in all the cases or interpretation.