( )

3.6 Negations of Conditional
Statements and De Morgan’s Laws
Negations
Negation of a Conditional Statement
~ p → q
( ) ≡ p∧ ~ q
Check Point 1
Write the negation of:
If you do not have a fever, you do not have the flu.
Solution
Label the simple statements.
p: You have a fever.
q: You have the flu.
You do not have a fever and you have the flu.
De Morgan’s Laws
De Morgan’s Laws
~ (p ∧ q) ≡ ~ p∨ ~ q
~ (p ∨ q) ≡ ~ p∧ ~ q

~ (p ∧ q) ≡ ~ p∨ ~ q
Check Point 2
Write a statement that is equivalent to:
It is not true that Bart Simpson and Tony Soprano are cartoon
characters.
Solution
Label the simple statements.
p: Bart Simpson is a cartoon character.
q: Tony Soprano is a cartoon character.
Bart Simpson is not a cartoon character or Tony Soprano is not a
cartoon character.

Check Point 3
Write a statement that is equivalent to:
It is not true that you leave by 5 pm or you do not arrive home on
time.
Solution
Label the simple statements.
p: You leave by 5 pm.
q: You arrive home on time.
You do not leave by 5 pm and you arrive home on time.
Check Point 4
Write the negation for
a) All horror movies are scary and some are funny.
b) Your workouts are strenuous or you do not get stronger.
Solution
a) All horror movies are scary and some are funny.
p: All horror movies are scary.
q: Some horror movies are funny.

Some horror movies are not scary or no horror movies are funny.
Some horror movies are not scary or none are funny.
Or the easy way…
It is not true that all horror movies are scary and some are funny.
b) Your workouts are strenuous or you do not get stronger.
p: Your workouts are strenuous.
q: You get stronger.
Your workouts are not strenuous and you get stronger.

Check Point 5
Write a statement that is equivalent to:
If it is not windy, we can swim and we cannot sail.
Solution
Identify the simple statements.
p: It is windy.
q: We can swim.
r: We can sail.
If we cannot swim or we can sail, then it is windy.