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(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

Let p = Thompson teaches this course.
Let q = I will get a passing grade.

Then the symbolic form should be ~q --> ~p. Completely valid!

Here's why...
p......q......~q......~p......~q --> ~p
T......T.......F........F..............T
T......F.......T........F..............F
F......T.......F........T..............T
F......F.......T........T..............T <---

Notice it is logically equivalent to p --> q (i.e., the truth table of ~q --> ~p is the same as the truth table of p --> q).

a landing airplane, moving in a straight line , passes over two points (p and q) which are 300 feet apart. when the airplane is above p, as seen from Q, its angle of elevation is 60 degress, and when above Q, as seen from p, its angle of elevation is 40 degress. at what distance from q will the airplane land?

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