Suppose the time is before symbolic logic was discovered and you were asked to prove:

That Antony is a funny guy ,given that:

If anyone is funny ,then he is happy. And ,there is someone who is funny but not happy.

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- Jul 10th 2011, 05:15 PMalexandroslogic
Suppose the time is before symbolic logic was discovered and you were asked to prove:

That Antony is a funny guy ,given that:

If anyone is funny ,then he is happy. And ,there is someone who is funny but not happy. - Jul 11th 2011, 07:40 AMMoeBleeRe: logic
- Jul 11th 2011, 11:01 AMalexandrosRe: logic
- Jul 11th 2011, 11:29 AMMoeBleeRe: logic
- Jul 11th 2011, 12:39 PMSorobanRe: logic
Hello, alexandros!

Where did this question come from?

It's badly written and it really doesn't make sense.

(Well, it*does*. . . but the conclusion is rather silly.)

Quote:

Suppose the time is before symbolic logic was discovered

and you were asked to prove:

. . [1] If anyone is funny, then he is happy.

. . [2] There is someone who is funny but not happy.

. . [3] Therefore, Antony is a funny guy.

I have to resort to symbolic logic to make my point.

We have: .$\displaystyle \text{(premise)}\:\to\:\text{(conclusion)}$

That is:. = . . . . . . $\displaystyle p\;\to\;q$

Statement [1] says: All funny people are happy.

Statement [2] says: There is one person who is funny but ishappy.*not*

. . That is, it istrue that all funny people are happy.*not*

The two statements contradict each other.

. . Hence, the premise is false.

So we have: .$\displaystyle F\;\to\;q$

And a false premise can imply.*anything*

Therefore: Antony is a funny guy.

- Jul 11th 2011, 12:47 PMMoeBleeRe: logic
You don't have to use any special symbols.

The statements "any person who is funny is happy" and "there is a funny but unhappy person" are contradictory, since they imply that there is a person who is happy and unhappy. And a contradiction implies any statement. So the statements "any person who is funny is happy" and "there is a funny but unhappy person" imply the statement "Antony is a funny person". - Jul 18th 2011, 06:39 PMalexandrosRe: logic