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# Implications - Contrapositive and Converse

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Contrapositive and converse are certain other statements which can be formed from a given statement with “if-then”.
For example, let us consider the following “if-then” statement.
If the physical environment changes, then the biological environment changes. Then the contrapositive of this statement is
If the biological environment does not change, then the physical environment does not change.
Note that both these statements convey the same meaning.

Statement : if p and q   ->  p -> q
Converse : if q then p  -> q -> p
Inverse : if not p then not q  ->  not p -> not q
Contra positive : if not q then not p -> not q -> 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
Solution :
If object is not polygon , then object is not square
If object is not polygon , then object is not triangle

Converse :
Converse of a given statement " if p , then q " is if  q, then p".
Statement :
If N is divisible by  6 , then N is divisible by 3
If N is divisible by 9 , then N is divisible by 3
Solution:
If N is divisible by  3 , then N is divisible by 6
If N is divisible by 3 , then N is divisible by 9

Inverse :
The inverse of a given statement " if p , then q " is "if ~p , then ~q" .
Statement:
If N is divisible by  6 , then N is divisible by 3
If N is divisible by 9 , then N is divisible by 3
Solution :
If N is not divisible by 6 , then N is not divisible by 3
If N is not divisible by 9 , then N is not divisible by 3

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Contrapositive, Converse, Inverse [00:10:07]
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