Statements of
Logic
Lesson 1.8
Conditional Statement Form
“If……then…….”
Declarative sentence
2 straight <„s are =
Conditional Form
If 2 <„s are straight <„s, then they are =.
“If………”
hypothesis
“….,then……”
conclusion
“If p then q”
p
Negation of p is:
q
“not p” ~p
It is raining. Negation: It is not raining.
p
~p
Negation of not p
~~p = p
It is not raining.
It is raining.
Not(not p) = p
p
Converse: (If q, then p) reverse
Inverse: (If ~p then ~q) negate
Contrapositive: (If ~q, then ~p)
negate and reverse
Use a Venn Diagram to solve problems.
Conditional Statement:
If I was born in St. Louis, then I was
born in Missouri.
Converse: If I was born in MO, then
I was born in St. Louis. (false) q p
MO.
MO.
St. L
St. LL
St.
Inverse: If I wasn‟t born in St.
Louis, then I wasn‟t born in MO.
(false, I could have been born in
MO.) ~p
~q
Contrapositive: If I
wasn‟t born in MO, then
I wasn‟t born in St.
Louis. (true) ~q ~p
Theorem 3: If a conditional statement
is true, then the contrapositive of the
statement is also true.
If p then q
If ~q then ~p
Symbol read as “implies”
Means equivalent to.
Statement and contrapositive are
logically equivalent.
Chain of reasoning:
If p
q
true
If q
r
true
then p
r
can conclude by transitive property
Write a conclusion from the given
statements. Rearrange to solve.
a
b
d
~c
~c
a
b
f
Hint: look for variables
that appear only once
(they start or stop the chain)
Those that appear
more are transitions.
Rearranged:
d
~c
~c
a
a
b
b
f
Conclusion: d
f