Question

Translate each argument into symbolic terms, then prove it is valid.
a. If all wealthy people are happy, then money can buy happiness. If money can buy happiness, then true love doesn’t exist. But true love exists. Therefore, not all wealthy people are happy.
b. If Clark is performing at the theater today, then everyone at the theater has a good time. If everyone at the theater has a good time, then Lois is not sad. Lois is sad. Therefore, Clark is not performing at the theater today.

Answer 1

Let p = all wealthy people are happy
let q = money can buy happiness
let r = true love exists
then (a) translates as follows:
1.) p -> q
2.) q -> ~r
3.) r
4.) ~p

Answer 2

The argument is valid by contrapositive
http://www.regentsprep.org/regents/math/geometry/gp2/lcontrap.htm

Since r is true, then r ->~q. Then ~q -> ~p.

Answer 3

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