Question

In: Advanced Math

Translate the following argument into symbolic form and determine weather it's logically correct by constructing a...

Translate the following argument into symbolic form and determine weather it's logically correct by constructing a truth table. Money causes all the world's troubles or money helps the poor. If money helps the poor, it is not the cause of all the worlds troubles. Money is the cause of all the world's troubles. Therefore, money does not help the poor. Please show how the problem was solved!

Expert Solution

Let us denote the predicates as follows:

The premises are that the following are TRUE:

Note that is logically equivalent to and is logically equivalent to . Since is true, we have is true if and only if is false.

Alternatively, here is the truth table. Here denotes TRUE and denotes FALSE.

P	Q	P OR Q	IF P THEN NOT Q
T	T	T	F
T	F	T	T
F	T	T	T
F	F	F	T

As the table shows, the only truth value of that ensures truth value (TRUE) for , , and , is that be FALSE.

Therefore, the argument is logically correct.

Colby Messinger answered 2 years ago

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