After a little bit of time learning discrete mathematics, I attempted this
This is the question
Determine whether or not the following arguments are valid. If they are valid, then state the rules of inference used to prove validity. If they are invalid, outline precisely why they are invalid.
a. If it is summer, then it is humid outside. If Santa is delivering presents, then it is not the case that it is hot and humid outside. It is currently hot outside and Santa is delivering presents. Therefore, it must not be summer.
b. If it is Thursday, then I do not have to go to class. I do not go to class. Therefore, it must be Thursday.
c. Everyone taking Computer loves math. Everyone taking Statistics loves math. Therefore, everyone in Statistics is taking Computer.
This is my answer
1A) Q = it is summer P = it is humid R = Santa is delivering presents Invalid R →( ¬Q ∧ ¬P) It is currently hot and Santa is delivering presents Therefore false B) Q = it is Thursday P = I have to go to class R = I went to class If it is Thursday then I do not have to go to class Q → ¬P I did not go to class ¬R It is Thursday Q 1 Q → ¬P 2 ¬R 3 Q 3 ¬R Modus Tollens C) Q = Taking computer P= loves math R = Taking Statistics Everyone taking Computer loves math Q ∧ P Everyone taking Stat 2507 loves math R ∧ P Therefore, everyone in statistics is taking comp R → Q 1 Q ∧ P 2 R ∧ P 3 R → Q 4 Q 1 Simplification 5 P 1 Simplification
Any help is appreciated thanks in advance