Truth Tables for the Conditional and Biconditional 3'4

1
Truth Tables for the Conditional and
Bi-conditional 3.4
In section 3.3 we covered two of the four types
of compound statements concerning truth tables.
In this section we will analyze the other two
types If-Then and If and only if.
2
Truth table of a conditional statement.
If p then q
antecedent
consequence
A conditional is only false when the antecedent
is true and the consequent is false
3
Construct a truth table for the following
All Ts tell you it is also a tautology
4
The truth value of a conditional statement does
not change if the antecedent and consequent are
reversed and both are negated.
is equivalent to
Use this fact to write the equivalent of the
statement
If a plant is not watered then, it wilts.
If a plant does not wilt, then it is being
watered.
5
Construct a truth table for the following
Then determine if the statement is a tautology.
A tautology is a compound statement that is
always true.
A self contradiction is a compound statement that
is always false.
6
Construct a truth table for the following
Then determine if the statement is a tautology.
Not a tautology
7
Construct a truth table for the following
Then determine if the statement is a tautology.
It is a tautology.
8
Truth table of a bi-conditional statement.
p if and only if q
A bi-conditional is true when the components have
the same truth value.
9
Construct a truth table for the following
10
Construct a truth table for the following
Tautology !!!!
11
Determine the truth value for the following
compound statement given the following
conditions p is false, q is true, and r is false.
12
Determine the truth value for the following
compound statement given the following
conditions p is false, q is true, and r is false.
13
Homework

• Pg 124
• 3 57
• Every other multiple of 3