Download Honors Geometry 2-2: Logic Conjunction Disjunction a

Honors Geometry
2-2: Logic
Use the given information to write two conjectures. One of your conjectures should be true; the
other should be possible, but false. Write a counterexample for the false conjecture.
1) Given: ∠1 ≅ ∠2
True Conjecture:
False Conjecture:
M
R
A
W
2) Given: AB + BC = AC
True Conjecture:
False Conjecture:
Use the given to determine if the following conjecture is true or false. If it is false write a
counterexample.
3) Given: 2 odd numbers
Conjecture: the sum of the two odd numbers will be even
4) Given: ∠1 and ∠2 are supplementary
Conjecture: ∠1 and ∠2 are a linear pair
Objective: determine the truth value of conjunctions and disjunctions (using truth tables)
Conjunction
a conjunction is a compound statement
formed by joining two or more statements
with the word and
Disjunction
a disjunction is a compound statement
formed by joining two or more statements
with the word or
p and q, p ᴧ q, p ∩ q
For a conjunction to be true, all parts must be true
p or q, p ᴠ q, p ᴜ q
For a disjunction to be true, only one part needs to be true
(to be false, all parts need to be false)
Determine the truth value using the following statements
p: The math office is in 201
q: The Bears home stadium is Lambeau Field
pᴧq
pᴠq
p and ~q
~p or ~q
Truth Tables
pᴧq
~p ᴧ q
pᴠq
(p ᴧ q) ᴠ r
Use the following statements to write a compound statement for each conjunction
and disjunction. Then find its truth value
p: 2 + 2 = 4
q: 3 noncolinear points determine a plane
r: vertical angles are adjacent angles that do not share interior points
p and q
p or r
p and ~q or r