# Solving Math Logic Problems: Adams, Brown & Clark

• haki
In summary, the conversation discusses two logic problems - one involving a murder and the other involving a Vulcan and two Romulans. After analyzing the statements made by the suspects in the murder case, it is concluded that Brown is the guilty party. In the second problem, it is determined that A is the Vulcan and B and C are Romulans. The solution to these problems were found to be relatively easy for the expert summarizer.
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.

Last edited:
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.

Thanks for the reply. Now I am at ease

## What is the purpose of solving math logic problems?

The purpose of solving math logic problems is to develop critical thinking skills and logical reasoning abilities. It also helps to sharpen problem-solving techniques and improve mathematical abilities.

## Who are Adams, Brown & Clark?

Adams, Brown & Clark are three mathematicians who have contributed significantly to the field of math logic. They are known for their work in developing logic-based problem-solving strategies.

## What are some common techniques for solving math logic problems?

Some common techniques for solving math logic problems include creating a diagram or chart, using trial and error, breaking the problem into smaller parts, and working backwards. It is also helpful to identify patterns and use deductive reasoning.

## How can I improve my skills in solving math logic problems?

The best way to improve your skills in solving math logic problems is to practice regularly. Start with simpler problems and gradually move on to more complex ones. It is also useful to study and learn different problem-solving strategies.

## Are there any resources available for learning how to solve math logic problems?

Yes, there are many resources available for learning how to solve math logic problems. These include textbooks, online tutorials and courses, and practice problems and worksheets. You can also seek help from a tutor or join a study group to improve your skills.

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