Logic 101
CONDITIONAL STATEMENT
If “_______p________”, then “________q_________”.
This is often read, “p implies q.”
The notation for this is:
pq
CONVERSE (of the original statement)
If “______q_______”, then “_________p________.”
Notation:
q p
INVERSE (of original statement)
If ”_______not p_____”, then “_______not q______.”
Notation:
not p  not q
CONTRAPOSITIVE (of the original statement)
If “______not q_____”, then “________not p_____.”
Notation:
not q  not p
LAW OF CONTRAPOSITIVES
A conditional statement and it’s contrapositive are either both true or both false.
Corollary: The converse and inverse of a conditional statement are either both
true or both false.
For the following conditional statements write the converse, inverse and
contrapositive. Then for all four determine which are true and which are false.
1) The ground is wet when it is raining. (assume the ‘ground’ is exposed)
2) If a polygon is a square, then it’s a rectangle.
3) An equilateral triangle is equiangular.
4) If I am in Georgia, then I am in the United States of America
5) If a tree is an Oak tree then it is a Red Oak tree.
6) If my name is Brian Perryman, then I am a teacher at Mountain View High School.