1. Truth tables 3.2 and 3.3 Constructing Truth tables
Evaluating individual statements to determine them T or F.

2. Truth tables p q p ∧ q T F p q p V q T F p ~p T F p q p→q T F p q p↔q
Negation ~p= not p p q
p ∧ q T F p q
p V q T F p ~p T F p q
p→q T F p q
p↔q T F

3. And ∧ is T only when both Tp q
p ∧ q T F
Or V is T when there is at least one T p q
p V q T F

4. If then and the iff p q p →q T F p q p ↔q T F
p → q is only F for T → F in that order.
Example: Consider:
If you study then you will get an A.
Let p = You study., and
Let q = You get an A.
So the above statement translates to p → q. Now lets consider the T→F case for p→q. That is suppose you DID study (p=T), but as is ended up, You DIDN’T get an A (q=F). In this case, the promise of the statement: of getting an A has been broken. A broken promise is a false statement. Thus T→F is F. Here p →q is false.
p ↔q is equiv. to p → q and q → p p q
p ↔q T F

5. Constructing a truth table
Complete the p, q, r columns
Complete columns for ~p, ~q, etc, if any exist
Complete columns for compound statements inside ()’s
Complete columns for connectives outside of the ()’s
The last column is the ANSWER column.

6. Evaluate the statement in symbolic form:
if it is given that p=T and q=F, and r=T

7. Answer:
Answer = F

8. Evaluate the English statement. That is, determine its truth value:
The 16th President of the U.S. was Lincoln or some presidents were women, and Lima is the capital of Peru.

9. The 16th Pres of the US was Lincoln or T
The 16th President of the U.S. was Lincoln or some presidents were women, and Lima is the capital of Peru Solution: First evaluate each simple statement.
The 16th Pres of the US was Lincoln or T
some presidents were women, and F
Lima is the capital of Peru.

10. Solution: replace with symbols and Ts and Fs
The 16th Pres of the US was Lincoln or some presidents were women, and Lima is the capital of Peru.
(T V F) T
T T T
Answer =T