Propositional Logic

1
Propositional Logic

• 6.4 Truth Tables for Arguments

2
Truth Tables for Arguments

• Symbolize the argument using letters for simple
  propositions.
• On one line, write the premises separated by
  single slashes, then the conclusion separated
  from the premises by a double slash.
• Apply TTFF and TFTF to each letter, then draw a
  truth table for each premise individually, and
  the conclusion individually.
• Look for a line where each premise is true but
  the conclusion is false. If there is such a line,
  the argument is invalid. If not, it is valid (it
  isnt possible for the conclusion to be false
  when the premises are true).
• Recall this applies only when there are 2 simple
  statements

3
Truth Tables for Arguments

• Step 1
• If Greg is right, then you are nuts. Oh, and Greg
  isnt right. So, you arent nuts.
• R ? N
• R
• N

4
Truth Tables for Arguments

• Step 2
• If Greg is right, then you are nuts. Oh, and Greg
  isnt right. So, you arent nuts.
• R ? N / R // N

5
Truth Tables for Arguments

• Step 3
• If Greg is right,
• R ? N / R // N

Step 4
Argument is invalid
F
T
F
It is possible for the premises to be true and
the conclusion false
T
T
T
T
F
F
T
T
F
F
T
Recall an argument is valid if true premises
guarantee the conclusion
T
T
F
F
T
T
F
T
T
T
F
F
F
F