## 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

1. gaurish

p -> q
r -> ~q
p -> s
r ->s

Not logical I guess.

• nkpithwa

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

• nkpithwa

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.

2. Anubhav Clancy Singh
3. Anubhav Clancy Singh