## Logical or Not?

**Ref: Ian Stewart’s Cabinet of Mathematical Curiosities**

If pigs had wings, they would fly.

Pigs don’t fly if the weather is bad.

If pigs had wings, the sensible person would carry an umbrella.

Therefore,

if the weather is bad, the sensible person would carry an umbrella.

*Is the deduction logically valid?*

🙂

(Prof Stewart has compiled/created a lot of fun for us :-))

-Nalin Pithwa

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## 5 Comments

p -> q

r -> ~q

p -> s

r ->s

Not logical I guess.

hey lets wait for some more responses..this is going to be real fun…

The logic is wrong. It the weather is bad, then pigs don’t fly. As a consequence, we don’t know whether they have wings. So, we don’t know whether to carry an umbrella.

It may seem strange that a deduction can be illogical when — as here the conclusion is entirely sensible. Actually, this is very common. For example, consider: 2+2=22=2 x 2 =4

is nonsense as far as logic goes, but it gives the right answer. All mathematicians know that you can give false proofs of correct statements. What you can’t do — if mathematics is logically consistent, as we fervently hope — is give correct proofs of false statements.

Since the weather is bad, the pigs don’t fly. Therefore they don’t have wings, implying that the sensible person doesn’t carry an umbrella. Therefore if the weather is bad, the sensible person wouldn’t carry an umbrella. Therefore the logic is wrong.

If the weather is bad, pigs won’t fly. If pigs won’t fly, then they don’t have wings. Therefore the sensible person would carry an umbrella, which proves the statement wrong. Therefore the logic is false.