2. FIRST, ANSWERS TO MINI-TEST
1. If Gregor plays first base, then the team will
lose.
G- Gregor plays first base
L – team will lose
G → L
2. The team will lose unless there is a miracle.
M- there is a miracle.
MvT
¬M →L
¬ L→M
3. The team will either lose or it won’t, but
Gregor will play first base regardless.
(Lv ¬ L)&G
4. Gregor’s mom will bake cookies if and only
if Gregor plays first base.
C- Gregor’s mom will bake cookies
C↔G
5. If there is a miracle, then Gregor’s mom will
not bake cookies.
M → ¬C
3. WHY?
• To evaluate sentences and arguments
• In particular, to see if the sentences is a tautology, contradiction or contingent
• To see if the set of sentences is logically equivalent or not
• To see if the set of sentences is consistent
• HOW? BY FINDING OUT SENTENCES’ TRUTH VALUES
4. WHAT TRUTH VALUES OF A SENTENCE
DEPEND ON?
• 1. Its parts
• 2. Its connectives
5. DEFINITIONS OF CONNECTIVES
DEFINE ITS TRUTH VALUES
• The following is important to remember!
We have five connectives, so its important to remember the truth values of those
connectoves
6. I. Negation
If A is true, ¬A is false
If A is false, ¬A is true
We only have 2 possible truth values = truth and false = 1 and 0
A ¬A
1 0
0 1
7. • II. Conjunction
• Conjunction is true only when its two conjuncts are true
A B A & B
1 1 1 1 1
1 0 1 0 0
0 1 0 0 1
0 0 0 0 0
8. • III. Disjunction
• Disjunction is true at least one disjunct is true
A B A V B
1 1 1 1 1
1 0 1 1 0
0 1 0 1 1
0 0 0 0 0
