Solving Math Logic Problems: Adams, Brown & Clark

[haki]

[Resolved]Math logic problem

I just want to know if I have applied correct reasoning to the following problems:

There are three suspects for a murder: Adams, Brown, and Clark.
Adams says "I didn't do it. The victim was an old acquaintance of
Brown's. But Clark hated him." Brown states "I didn't do it. I didn't
even know the guy. Besides I was out of town all that week." Clark
says "I didn't do it. I saw both Adams and Brown downtown with
the victim that day; one of them must have done it." Assume that
the two innocent men are telling the truth, but that the guilty man
might not be. Who did it?

Is it really that simple? I defined just one predicate Knows Victim - K(x)

A: K(B) //says B knew the victim
B: NOT K(B) //says he didnt knew the victim
C: K(B) // said that B was with victim

Therefore the only explanation is that A and C are telling the truth and C was lying, he wasn't out of town was he?

And second

There are 3 persons, A,B and C. One of them is a Vulcan who always tells the truth the second two are Romulans who always lie.

They gave the following statements:

A: B is a Romulan if and only if C is not Vulcan.
B: I am not Vulcan when C is a Vulcan.
C: A is not a Vulcan.

I introduced the predicate ... is Romulan R(x) and ... is Vulcan V(x)

A: R(b) <-> NOT V(c)
B: NOT V(b) <-> V(c)
C: NOT V(a)

Now I stated that if somebody is NOT Vulcan then he must be Romulan, therefore I get

A: R(b) <-> R(c)
B: R(b) <-> NOT R(c)
C: R(a)

now A and B are contradictory, therefore one of them must be a liar and one of them must be telling the truth, but since only one is telling the truth then C must be telling a lie, therefore R(a) is a lie and because of the V(a) is true. Mr. A is Vulcan and B and C are Romulans.

Is this correct. I found this tasks to be super easy, I get a bit fishy when I solve something in math with relative ease.

 

[arildno]

In ordinary usage, I wouldn't say that "knowing a person" is the same as "being with a person". (They may merely have been in physical proximity of each other).

Note that Adams and Brown necessarily contradict each other ("old acquaintance" contradicts "don't even know the guy")

Thus, by hypothesis, C NECESSARILY speaks the truth!
Thus, it is true that he saw Brown downtown, and thus Brown is lying when saying he was out of town all day.
Hence, Brown is the killer.

 

[haki]

Thanks for the reply. Now I am at ease