Transcript Section 1.2 Evaluating Compound Propositions

Section 1.2
Evaluating Compound Propositions
Vocabulary Words
• compound proposition
In-Class Activity #1
• Get in groups of 3 or 4 students.
– By next week I’m going to ask you to try to
settle into regular groups that you will use each
day for the first half of the semester.
• Again, each person should print their name
at the top of the paper I will hand out.
• As a group, complete Part One
Activity
• Let
– m = Juan is a math major
– c = Juan is a computer science major
• How would we write
– Juan is a math major but not a computer science
major
Activity
• Let
– s = stocks are increasing
– i = interest rates are steady
• How would we write
– Stocks are increasing while interest rates are
steady
– Neither are stocks increasing nor are interest
rates steady
Activity
• Neither are stocks increasing nor are
interest rates steady.
• It’s pretty common for me to hear several
different answers for this one.
• How can we determine if two different
answers are equivalent?
Truth Tables
• A truth table shows the relationship
between various (often related) statements.
• It’s size depends on the number of
independent variables represented in the
statements
– N independent atomic formulae (variables) 
2N rows
One possibility
p
q
T
T
T
F
F
T
F
F
¬p¬q
Order of Operations
• Just like there is an order of operations with
arithmetic (remember PEMDAS?) there is
an order of operation with logic.
¬


One possibility
p
q
T
T
T
F
F
T
F
F
¬p¬q
One possibility
p
q
T
T
T
F
F
T
F
F
¬p
¬q
¬p¬q
Activity #2
• Let’s see which variations are equivelent.
Variation 1
p
q
T
T
T
F
F
T
F
F
¬p
¬q
¬p¬q
Variation 2
p
q
T
T
T
F
F
T
F
F
p q
¬ (p  q)
Variation 3
p
q
T
T
T
F
F
T
F
F
p q
¬ (p  q)
“Bigger” Compound Propositions
• While the examples we just looked at were
“compound” because they had more than
one operator, they still dealt with two
variables.
• But lots of times when we use this phrase
we are referring to three or more variables.
Activity #3
• Let
– h = John is healthy
– w = John is wealthy
– s = John is wise
Activity #3
Write compound propositions representing
1.
2.
3.
4.
John is healthy and wealthy but not wise
John is not wealthy but he is healthy and wise
John is neither healthy, wealthy, nor wise
John is neither wealthy nor wise, but he is
healthy.
5. John is wealthy, but he is not both healthy and
wise.
How do we build truth tables for
these larger compound propositions?
Truth Tables
• A truth table shows the relationship
between various (often related) statements.
• It’s size depends on the number of
independent variables represented in the
statements
– N independent atomic formulae (variables) 
2N rows
A three variable truth table
p
q
r
T
T
T
T
T
F
T
F
T
T
F
F
F
T
T
F
T
F
F
F
T
F
F
F
p qr
Activity #4
A three variable truth table
p
q
r
T
T
T
T
T
F
T
F
T
T
F
F
F
T
T
F
T
F
F
F
T
F
F
F
p  (¬q  r )
A three variable truth table
p
q
r
pqpr
T
T
T
(1)
T
T
F
(2)
T
F
T
(3)
T
F
F
(4)
F
T
T
(5)
F
T
F
(6)
F
F
T
(7)
F
F
F
(8)