1. 1.8 Statements of LOGIC
Conditional Statement Form
“If……then…….”

2. Declarative sentence Two straight angles are congruent
Conditional Form If two angles are straight angles, then they are congruent.

3. Negation of p is: “not p” ~p
“If………” hypothesis
“….,then……” conclusion
“If p then q” p q
Negation of p is: “not p” ~p
It is raining. Negation: It is not raining.
p ~p

4. Converse: (If q, then p) reverse Inverse: (If ~p then ~q) negate
Negation of not p ~~p = p
~p: It is not raining. p: It is raining.
Not(not p) = p It is not NOT raining, therefore, it IS raining.
Converse: (If q, then p) reverse
Inverse: (If ~p then ~q) negate
Contrapositive: (If ~q, then ~p)
negate and reverse

5. Conditional Statement:
If I was born in St. Louis, then I was born in Missouri. p q
Converse: If I was born in MO, then I was born in St. Louis. (false) q p

6. Inverse: If I wasn’t born in St. Louis, then I wasn’t born in MO
Inverse: If I wasn’t born in St. Louis, then I wasn’t born in MO. (false, I could have been born in Hannibal, MO.) ~p ~q
Contrapositive: If I wasn’t born in MO, then I wasn’t born in St. Louis. (true) ~q ~p

7. If Blake is a member of the Basha High soccer team, then he is a student at Basha High.
Write the…
Converse
Inverse
Contrapositive
State the truth value of the new statements!

8. 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.

9. Chain of reasoning:
If p q true
If q r true
then p r
can conclude by transitive property

10. 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.

11. Rearranged:
d ~c
~c a
a b
b f
Conclusion: d f