MATH 1630 – Outline for 3.3
3.3 – The Conditional Statement and Circuits
Definition:
Conditional Statement – If p, then q
(p = antecedent, q = consequent)
I. Truth Table for p
→
q
p q p
→
q
T T T
T F F
F T T
F F T
II. Determine the truth value of a compound statement using all 4 connectives (And,
Or, Not, If…then)
a.)
qrp
→
∧
)~(
b.) )()( qprq
∨
→
→
III. Build truth tables for compound statements using all 4 connectives and be able
to determine a tautology
a.) pqp
→
→
)~ (
b.) )()( qpqp
∨
→
∧
IV. Negation of p
→
q (this is the third type of negation that we will cover)
qpqp ~)(~
∧
≡
→
Note: the negation of If p, then q becomes p AND not q
V. Circuits
Key: Determine all of the paths through which electricity can flow, combine them
into a compound statement, and then simplify (see table on p.119).