Conditional  ( p  q ):
If a number is an integer, then it is a natural number.
Hypothesis:  	If a number is an integer,
Conclusion:	then it is a natural number.

Converse  (q  p ):
If it is a natural number, then the number is an integer.
Hypothesis:	If it is a natural number,
Conclusion:	then the number is an integer.

Inverse  ( p   q ):
If a number is not an integer, then it is not a natural number.
Hypothesis:	If a number is not an integer, 
Conclusion:	then it is not a natural number.

Contrapositive   ( q   p ):
If the number is not a natural number, then the number is not an integer.
Hypothesis: 	 If the number is not a natural number,
Conclusion:	 then the number is not an integer.

Bi-conditional: When you combine a conditional statement and its converse you create a bi-conditional statement.

A number is an integer if and only if it is a natural number.
(If conditional) A number is an integer if and only if
(If converse) it is a natural number.