Expert: Sherry Wallin - 4/16/2009

Question
QUESTION: help me for this some hard question about logic

1. A triangle has at least three sides.
2. A triangle has at most three sides.
3. Every mathematician 10 feet tall loves to dance.
4. There exists a mathematician 10 feet tall who loves to dance.
5. The moon is made of ice if and only if the Earth is made of fire.
6. If ice is hot, then it is cool.
7. If 3 is even then 4 is prime.
8. If every prime number is odd, then 5 is prime.
9. If 5 is prime, then every prime number is odd.
10. No man is an island, therefore a square is a polygon.


pls help me... thnx

ANSWER: Hi lhan~
   First I need to know what the question is! Are you asked to prove these statements or are you suppose to determine if they are true or false or not truth value??

---------- FOLLOW-UP ----------

QUESTION: i want you to prove your answer ... plsss... tnx

Answer
I think they are wanting you to assign truth values to these statements and then decide it they are true or false. This can only be done to those statements that are propositions. So the first step is to decide if each is a proposition, that is if each statement can have a truth value assigned to it.

1 - true since a triangle has exactly 3 sides so to say at least 3 sides is the same as saying 3 or more and it has 3 so it is true
Another way to think of this is: if it is a triangle then it has at least 3 sides. T->T  which is true
2 - at most 3 sides means less than or equal to 3 sides, so as in 1 above this is true (same alternate as above)
3 -  If you are a 10ft mathematician then you love to dance. I think it is same to assume that there aren't any 10ft mathematicians so we have F -> T or F, doesn't matter, both results in a true value
4 -there is no truth value to be assigned here, note that this says that there is a person who is a mathematician and is 10 ft tall and loves to dance.
5- says If the moon is made of ice then the earth is made of fire and if the earth is made of fire then the moon is made of ice. By the way both statements: the earth is made of fire" and "the moon is made of ice" are false statements and this translates into F <-> F which in a truth table is equivalent to (F->F)^(F->F) which is equivalent to F-> F which is ALWAYS true
6- the statement "if ice is hot" is false so in a conditional truth table F-> anything is true
7 - if 3 is even is false so again it doesn't matter what the "then" part is because in conditional statements if the antecedent is false both when the consequent is true or false the whole statement is true
8 - same thing for this one because it isn't true that every prime number is odd so the antecedent is false thus the whole conditional is true
9- if 5 is prime is a true statement so it does depend on the truth value of the consequent since if the consequent is false then T->F is always false. In this case "every prime number is odd" is false so we have T -> F which is ALWAYS false
10 - "no man is an island is a true statement so again it depends on the truth value of the consequent which "a square is a polygon" is a true statement and we have T->T which is true.