Problem 4. What is the structure of the following argument? If the Sun orbits th

Question

Problem 4. What is the structure of the following argument?

If the Sun orbits the Earth, then the Moon is made of cheese; If the Moon is made of cheese, then Homer Simpson is an alien; If Homer Simpson is an alien, then 2+2 = 5; 2+2 = 4, not 5. Therefore, the Sun does not orbit the Earth. (Q13) ?

A: p q; p. Therefore, q.

B: (p | q) r; !r. Therefore, !p & !q.

C: p & q. Therefore, p | q.

D: p q; q r; r s; !s. Therefore, !p.

E: p q; q r; r s; p. Therefore, s.

F: p q; !p. Therefore, !q.

G: (p | q) r; r. Therefore, p | q.

H: p | q; !p. Therefore, q.

Is the argument logically valid? (Q14) ? A: no B: yes

Explanation / Answer

p->sun orbits the earth

q->moon is made up of cheese

r->homer simpson is an alien

s->2+2=5.

if sun orbits the earth then moon is made of cheese:p -> q

if the moon is made of cheese the homer simpson is an alien :q ->r so p -> q ->r

if homer simpson is an alien then 2+2=5:r -> s so p ->q ->r ->s

but 2+2=4 therefore !s

therefore sun does not orbits earth i.e. !p

so the final structure is

d:p -> q;q -> r;e -> s; !s . Therefore , !p.

now coming to the second part

if p then q then r then s

p -> s; !s therefore !p {By using Modus Tollens}

that's why the argument is always valid

argument is valid. B:yes

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