Use a truth table to test the
validity of the following
argument.
If you are on the student council,
then you must maintain at least a
B average.
You are not on the student
council.
Therefore, you do not maintain a
B average.
(1 point)
valid
invalid
To test the validity of the argument using a truth table, we need to assign truth values to the premises and the conclusion:
Let p = "You are on the student council."
Let q = "You maintain at least a B average."
The premises are:
1. If p, then q. (p → q)
2. Not p. (~p)
The conclusion is:
3. Not q. (~q)
We can construct a truth table to test the validity of the argument:
| p | q | ~p | p → q | ~p → ~q |
|----|----|----|-------|---------|
| T | T | F | T | F |
| T | F | F | F | T |
| F | T | T | T | T |
| F | F | T | T | T |
From the truth table, we can see that when "You are not on the student council" (~p) is true and "You do not maintain a B average" (~q) is also true, the argument is invalid. Therefore, the argument is invalid.