# A few logic puzzles..

The following four arguments all appear to be invalid. Briefly explain why in each case.

a)
i) It is true that: No mermaids are found in the Thames
ii) It is false that: All mermaids are found in the Thames
iii) It is true that: Some mermaids are not found in the Thames.
iv) It is true that: There is at least one mermaid.

b)
i) All those who are the most hungry eat the most
ii) All those who eat the least are the most hungry
iii) Therefore those who eat the least eat the most.

c) You can’t believe what the Chairman of the gasboard says about the importance of higher salaries for those in management. As a Chairman himself, he would naturally be in favour of increasing management salaries.

d)
i) The girl in the photograph is my grandmother.
ii) The girl in the photograph is six years old
iii) So my grandmother is six years old.

Please reference the ones you are answering. Enjoy!

I think perhaps you’re missing the point of the mermaid one. The argument is invalid because it has managed to define mermaids into existence. The task is to find the inconsistency in the sentences (which you’ve basically done).

I see the flaw lying in point i) and onwards. If we look at the negations of each of the statements we can see where the flaw arises. While point i) does look convincing we can see that the opposite of the statement is:

“It is false that: Some mermaids are found in the Thames”

Before we’ve even started it’s assumed that there are some mermaids! We then goto the next statement which reversed looks like:

“It is true that: All mermaids are not found in the Thames.”

ALL MERMAIDS NOW! We’re just creating mermaids out of nowhere!

NB: I don’t have the answers for these, they were in an Oxford Uni entrance paper.

Numbah 2)

The two premises are inconsistant. And because of that the conclusion implies a contradiction. which makes it invalid.

Numbah 3)

Thats kinda ad homenem informal falacy. Your attackin the person rather then the argument. Of course its LIKLEY that the chairman is kinda biased in raising salaries, i needs sum other premises to back that up to make it valid.

Number 4)

As it is, i would have to say that the fouth one IS valid. It is logically possible that your grandmother is six years old… although its not something i see being physically possible. By just saying that the girl in the photograph is 6 years old, we have no way of knowing if it is ment that the girl was 6 years old IN the photograph or that the girl in the photograph is 6 years old NOW. Im not sure if you can say its invalid just because of lack of information.

Number 4.)

The girl in the photo is your grandmother.
The girl in the picture is six years old.
Your grandmother was six years old at the time of the photograph.

a) Statement iii contradicts the first two. The first two say that there are no mermaids in the Thames. Statement iii says that some mermaids are not in the Thames. And from this you could say that there are some mermaids in the Thames. So you can’t really deduct anything from statement iii.