Use the truth table test of validity to determine whether or not the following arguments are valid or invalid.
1.
1. A v B
2. B
3. ? ~A
2.
1. A ? B
2. ? A v B
3.
1. ~C
2. ? ~(C v A)
4.
1. (A v B) ? (A v C)
2. ~A
3. ? B v C
5.
1. R ? (T v S)
2. T
3. ? ~S
6.
1. A v B
2. ? A ? B
7.
1. ~(A ? B)
2. ? ~A v ~B
8.
1. ~(A v B)
2. ? ~A v ~B
9.
1. (R v S) ? ~D
2. ~R
3. ? S ? ~D
1. Invalid
2. Valid
3. Invalid
4. Valid
A B C (A v B) ? (A v C) ~A B v C
T T T T T T F T
T T F T T T F T
T F T T T T F T
T F F T T T F F
F T T T T T T T
F T F T F F T T
F F T F F T T T
F F F F F F T F
Answers to exercises
216
5. Invalid
R T S R ? (T v S) T ~S
T T T T T T F
T T F T T T T
T F T T T F F
T F F F F F T
F T T F T T F
F T F F T T T
F F T F T F F
F F F F F F T
6. Invalid
7. Valid
8. Valid
A B ~(A v B) ~A v ~B
T T F T F F F
T F F T F T T
F T F T T T F
F F T F T T T
9. Valid
D R S (R v S) ? ~D ~R S ? ~D
T T T T F F F F
T T F T F F F F
T F T T F F T F
T F F F F F T F
F T T T T T F T
F T F T T T F F
F F T T T T T T
F F F F F T F F
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