Maths Class 11 Chapter 14. Mathematical reasoning | Page 5

o
Both are true or false together o Both sufficient and necessary condition. E. g. Krishna will eat if and only if food is Apple.
Contrapositive, Converse, Inverse Statement: if p then q Converse: if q then p Inverse: if not p then not q Contrapositive: if not q then not p If a statement is true, contrapositive is also true. If converse is true, the inverse is also logically true.
Contrapositive Contra positive of a given statement“ if p, then q” is if ~ q, then ~ p.
Statement: If object is square, then object is Polygon If object is triangle, then object is Polygon
Contra positive: If object is not polygon, then it is not Square If object is not polygon, then it is not Triangle
Statement:
If p à then q
Contra positive:
If ~ q à then ~ p
If statement is true then contra positive is also true.