Notes: 2-3 and 2-4 *Not all symbols appear correctly in notes

2-3 Deductive Reasoning
CS can be written using notations
- “p” represents the hypothesis
- “q” if the conclusion
- “  “ is read as “implies”

CS: If the sun is out, then the weather is good. p q
p q
Converse: If the weather is good, then the sun is out q p
q p
BS: If p, then q, and if q then p OR p q OR p if and only if q
Try: p= the value of x is -5 q= the absolute value of x is 5
a. write p q in words
b. write q p in words
c. is pq true?
To write the inverse and contrapositive, you need to be able to negate the the statement symbolically. We use the (~) symbol to do so.
Statement: ∟3 measures 90 ∟3 is not acute
Symbol: p q
Negation: ∟3 does not measure 90 ∟3 is acute
Symbol: ~p ~q
The inverse of p q : ~p ~q If ∟3 does not measure 90, then ∟3 is acute
The contrapos of p q: ~q~p If ∟3 is acute, then ∟3 does not measure 90
For me: ex. 2 pg 88

Deductive Reasoning- uses facts, def., and properties in logical order to write and argument
Laws of Deductive Reasoning:
Law of Detachment: If pq is a true conditional statement and p is true, then q is true
(ex 4 on pg 89)
Law of Syllogism: if pq and qr are true conditional statements, then p r is true
Together ex 5 and ex 6,
prac 1-7 pg 91

2-4 Reasoning with Properties from Algebra
Addition Property: If a=b, then a+c= b+c
Subtraction: If a=b, then a-c=b-c
Multiplication: If a=b, thenac=bc
Division: If a=b and c not equal to 0, then a/c=b/c
Reflexive: For any real number a, a=a
-Geometric: segment AB= segment AB;;;;; m< A= m Symmetric: If a=b, then b=a
-Geometric: If AB=CD, then CD=AB;;;;; If m Transitive: If a=b, and b=c, then a=c
-Geo: If AB=CD and CD=ED, then AB=EF;;;; If m then m Substitution: If a=b, then a can be substituted for b in any equation or expression
Example 1 and 2 pg 96; 4 and 5 pg 98
Guided practice 1-9 pg 99