Translate the following sentence into symbolic form."I'll go to the football game with you as long as you buy me pizza and it isn't too cold."

Question

This is contemporary mathematics.  Something to do with conditional statements and truth tables.

Full question:  Translate the following sentence into symbolic form.  Clearly state what your letters represent.  "I'll go to the football game with you as long as you buy me pizza and it isn't too cold."

 

Answer 1

First, let's clearly state what our letters represent. I will assign letters to various parts of the sentence as an example:

 

F = I will go to the football game with you

P = you buy me pizza

C = it is too cold

 

 

Second, let's write the sentence using the assigned letters and designated symbols. ***Note: Sometimes there are different symbols used by different classes, but they actually mean the same thing. Your class may ask you to use a different symbol than what I use.

 

P & ~C ≡ F

 

& = Conjunction or "and"

~ = Negation or "not"

≡ = Equivalence or "if and only if"

 

 

Finally, a truth table is used to determine the truth or falsity of the sentence based on the truth or falsity of the individual expressions. If there are two expressions (as in this case: "P & ~C" and "F"), the table is four lines long. In order to ensure all combinations are expressed, start by labeling the first expression ("P & ~C") with 2 truths followed by 2 falsities; then, label the second variable ("F") by alternating 1 truth with 1 falsity. Finally, take into account the combined truths and falsities to determine the truth value of the entire sentence.

 

P & ~C     F          P & ~C ≡ F

   T          T                  T      If and only if you buy me pizza and it isn't too cold, I will go to the football game with you.

   T          F                  F      If and only if you buy me pizza and it isn't too cold, I will not go to the football game with you.

   F          T                  F      If and only if you don't buy me pizza and it is too cold, I will go to the football game with you.

   F          F                  T      If and only if you don't buy me pizza and it is too cold, I will not go to the football game with you.