(a) translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
If Nicholas Thompson teaches this course, then I will get a passing grade.
I did not get a passing grade.
∴ Nicholas Thompson did not teach the course.
correct! this is called the contrapositive.
p->q ≡ ~q->~p
I will leave it to you to prove the identity with truth tables.
a swimming pool is built as follow;
the top view is a rectangle 12ft by 30ft. the pool is 4 feet deep at the shallow end and 9 feet at the deep end. the sides walls are as shown. how many square ft of tile will it take to tile the two side walls and both end walls?
To translate the given argument into symbolic form, we can assign variables to represent the different statements involved. Let's use:
P: Nicholas Thompson teaches this course.
Q: I will get a passing grade.
The argument can now be translated as follows:
If P, then Q.
Not Q.
Therefore, not P.
Now, to determine if the argument is valid or invalid, we can compare it to a standard form or use a truth table. Let's use a truth table in this case:
| P | Q | If P, then Q | Not Q | Not P |
|---|---|--------------|-------|-------|
| T | T | T | F | F |
| T | F | F | T | F |
| F | T | T | F | T |
| F | F | T | T | T |
In the truth table, we observe that there is a row in which the premises (the first two columns) are true, but the conclusion (the last column) is false. This means that the argument is invalid, as we have found a counterexample that demonstrates that the conclusion does not necessarily follow from the premises.