1. 2.3 Using Deductive Reasoning to Verify Conjectures
Geometry

2. Reminders Statement _________ statement ______________
______________ (iff)
Symbols
p → q
q → p
~p → ~q
~q → ~p
p ↔ q

3. Ex 1: Given: p – it is 5th period q – it is time for lunch
Write p→q.
Write ~p.
Write p↔q.
Is p↔q true?

4. Laws of Deductive Reasoning
1. Law of _______________
2. Law of Syllogism

5. Law of Detachment
If a statement p→q is ________ and a ________ statement p is given, then a third statement q _____________.
Given: p→q p q
Ex2): 1. If x is even, then x2 is even.
2. x = What statement follows?

6. Ex.3 & 4 Given: 1. If it is raining, then the ground is wet.
2. It is raining What follows?
Given: 1. If an < is between 0o and 90o, then it is acute.
2. <B is acute What follows?

7. Law of Syllogism
If p→q is _________ and q→r is ________, then p→r _____________.
Given: p→q
q→r
p→r

8. Ex 4:
Given: 1. If Tony is sick on Friday, then he cannot play football.
2. If Tony cannot play football, then the team will lose.
What statement follows? q
p→q
q→r
p→r p r

9. Ex 5: Given: p→q q→s r→s r→q What follows? . Given: q→r s→t r→s p→q

10. Assignment