Here I have such a question related to laws of inference. The question asks to prove using the laws of inference (these rules) that the following facts give a certain conclusion. So the question is:
All the students that studied passed the exam. Ann passed the exam.So, I can say that Ann studied.
What I thought is: Generally we are talking about students. The statements are:
P(x): "x studied" and Q(x): "x passed the exam"
So the statment:
- All the students that studied passed the exam is $\forall x(P(x) \to Q(x))$
- Ann passed the exam is $Q(Ana)$
So I must prove that the conclusion is $P(Ana)$. The problem is I do not know what law of inference to use. The conclusion is obvious, but I do not understand how to show this thing using discrete math tools. Can you please help me ? Thanks.