Truth Table Test - Short Form

The truth-table test for validity works with arguments of any level of complexity.

For every additional component proposition, we double the number of lines we need. So the problem gets worse exponentially: for an argument with n components, we need a table with 2n lines. Fortunately, there's a shorter and more efficient way to use the truth table test of validity. Because we want to know whether the conclusion can be false if the premises are true, we need only consider those lines in a truth table where the conclusion is false. If we can find those lines without writing out the entire truth table, we can save a great deal of effort.


Comprehension Questions

1 The truth values for the first premise of the following argument are
Premise
Premise
Conclusion
(A v B) > (A . B)
~(A v B)
~(A . B)
A
T
T
F
F
B
T
F
T
F
a) T F F T
b) F T T F
c) F F T T
d) T F T F
2 The truth values for the second premise of the following argument are:
Premise
Premise
Conclusion
(A v B) > (A . B)
~(A v B)
~(A . B)
A
T
T
F
F
B
T
F
T
F
a) T T T F
b) T F T F
c) F F F T
d) T F F T
3 The truth values for the conclusion of the following argument are:
Premise
Premise
Conclusion
(A v B) > (A . B)
~(A v B)
~(A . B)
A
T
T
F
F
B
T
F
T
F
a) T F F F
b) F T T T
c) T F T F
d) T F F T
4 Is the argument below valid or invalid?
Premise
Premise
Conclusion
(A v B) > (A . B)
~(A v B)
~(A . B)
a) invalid
b) valid
5 The truth values for the first premise of the following argument are:
Premise
Premise
Conclusion
(A > (B > C))
(B > (A > C))
(B v A) > C
A
T
T
T
T
F
F
F
F
B
T
T
F
F
T
T
F
F
C
T
F
T
F
T
F
T
F
a) T F T T T F T T
b) F T T T T F F T
c) F T T F T F T F
d) T F T T T T T T
6 The truth values for the second premise of the following argument are:
Premise
Premise
Conclusion
(A > (B > C))
(B > (A > C))
(B v A) > C
A
T
T
T
T
F
F
F
F
B
T
T
F
F
T
T
F
F
C
T
F
T
F
T
F
T
F
a) T F T T T F T T
b) F T T T T F F T
c) F T T F T F T F
d) T F T T T T T T
7 The truth values for the conclusion of the following argument are:
Premise
Premise
Conclusion
(A > (B > C))
(B > (A > C))
(B v A) > C
A
T
T
T
T
F
F
F
F
B
T
T
F
F
T
T
F
F
C
T
F
T
F
T
F
T
F
a) T T T F T F T T
b) F T F F T F F T
c) T F T F T F T T
d) T F T T T T T T
8 Is the argument below valid or invalid?
Premise
Premise
Conclusion
(A > (B > C))
(B > (A > C))
(B v A) > C
a) invalid
b) valid


Proof

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