Type your question hereQ1 - Q3 are word problems given as a sequence of hypothes

Question

Type your question hereQ1 - Q3 are word problems given as a sequence of hypotheses/ premises ending with "Therefore conclusion". Show that each
word problem is a valid argument.
Use rules of inference to show steps and reasons in the proof.

1) If I take a bus or subway then I'll be late for my appointment.
If I take a taxi then I will be on time for my appointment and
I will be broke. If I don't take the subway and don't take a bus
then I will take a taxi. I will not be late for the appointment.
Therefore, I will be broke.

2) If the interest rates drop then the housing market will improve.
Either the federal discount rate will drop or construction will
decrease. Interest rates will drop and utility prices will go down.
Either construction increases or the housing market does not improve.
Therefore, the federal discount rate will drop.

3) It is cold and not sunny today. We'll go for a run only if it
is sunny. If we do not go for a run then we will go for a walk on
the beach. We will watch a movie or we will not go for a walk on
the beach. Therefore, we will watch a movie.

please step by step and make sure they are correct thank you very much . no table but in a form of modum pollens tollen etc

final statement and proof thanks

Explanation / Answer

~A is not of A below.

(a)

A: I take a bus

B: I take subway

C: I'll be late for my appointment

D: I take a taxi

E: I will be broke

Given sentences are:

A or B -> C

D -> ~C and E

~A and ~B -> D

~C

We need to find if ~C -> E.

~C -> ~(A or B). Thus ~C -> ~A and ~B

But ~A and ~B -> D. and D -> ~C and E.

But ~C is true, this E is true. Therefore ~C -> E.

(b)

A: the interest rates drop

B: housing market will improve

C: federal discount rate will drop

D: construction will decrease

E: utility prices will go down

Given:

A -> B

C or D

A and E

~D or ~B

We need to prove that C is true.

A is true. Thus B is true. ~B is false. Since ~D or ~B is true, ~D true. Thus D is false.

Also C or D should be true. Thus C should be true.

Therefore given statement is true.

(c)

A: It is cold

B: It is not sunny

C: We'll go for a run

D: we will go for a walk

E: We will watch a movie

Given statements are:

A and B

C <-> ~B

~C -> D

E or ~D

A is true and B is true. Since B is true, therefore ~B is false. Thus C is false. Thus ~C is true. This implies D is true. Thus ~D is false.

Since E or ~D should be true, therefore E is true.

Therefore given statement is true.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.