1. TRUTH TABLES

2. T F Truth Table for p  q p q p  q
Recall that conditional is a compound statement of the form “if p then q”.
Think of a conditional as a promise. If I don’t keep my promise, in other words q is false, then the conditional is false if the premise is true.
If I keep my promise, that is q is true, and the premise is true, then the conditional is true.
When the premise is false (i.e. p is false), then there was no promise. Hence by default the conditional is true. p q
p  q T F

3. T F Truth Table for p ^ q p q p ^ q
Recall that the conjunction is the joining of two statements with the word “and”.
For p ^ q to be true, then both statements p, q, must be true.
If either statement or if both statements are false, then the conjunction is false. p q
p ^ q T F

4. T F Truth Table for p v q p q p v q
Recall that a disjunction is the joining of two statements with the word “or”.
For a disjunction to be true, at least one of the statements must be true.
A disjunction is only false, if both statements are false. p q
p v q T F

5. T F p ~p Truth Table for ~p
Recall that the negation of a statement is the denial of the statement.
If the statement p is true, the negation of p, i.e. ~p is false.
If the statement p is false, then ~p is true.
Note that since the statement p could be true or false, we have 2 rows in the truth table. p ~p T F

6. Equivalent Expressions
Equivalent expressions are symbolic expressions that have identical truth values for each corresponding entry in a truth table.
Hence ~(~p) ≡ p.
The symbol ≡ means equivalent to. p ~p
~(~p) T F

7. Negation of the Conditional
Here we look at the negation of the conditional.
Note that the 4th and 6th columns are identical.
Hence p ^ ~q is equivalent to ~(p  q). p q ~q
p ^ ~q
p  q
~(p  q) T F