Question

Translate the following arguments into symbolic form and use the first eight rules of inference to derive the conclusion of each. Use the letters in the order in which they are listed.

If half the nation suffers from depression, then if either the insurance companies have their way or the psychiatrists have their way, then everyone will be taking antidepressant drugs. If either half the nation suffers from depression or sufferers want a real cure, then it is not the case that everyone will be taking antidepressant drugs. Half the nation suffers from depression. Therefore, it is not the case that either the insurance companies or the psychiatrists will have their way. (H, I, P, E, W )

Answer 1

Follows are the solution to this question:

Step-by-step explanation:

H = It is the half of nation is depressed

J = It is the Insurance, which is provide by the way.

P = It is the phychiatris way

E = An antidepressant drugs, which can be used by everyone

w = The patients want real treatment

Symbolic form can be defined as follows:

`H ((IVP) \varepsilon ) \\ (H V W) (\varepsilon )\\ H`

Substance: (IVP)

The evidence:

`i). H \supset ((IVP)\supset \varepsilon ) \\ii). (HVW) \supset \wedge \varepsilon \\iii). H \\iv). (IVP) \supset \varepsilon [ 1,3 Modus Porers] \\v). HVW [ 3 , adddition] \\vi). \wedge \varepsilon [2, 5 mp] \\vii). \wedge (IVP) [4,6 Modus tollens]`

So it's true that conclusion.

`\left\begin{array}{ccc}mp&addition&mt\\p \ \ \ \ q&p&p\ \ \ \ q\\(p)/(q) & p \vee q & ( q)/(p)\end{array}\right`