# Rules of inference

## For each of these collections of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises.

As with the previous examples, there are two main things we need to solve this exercise. First, we need to know the rules of inference so we can apply them. Second, we need to identify whether we must use propositional variables or predicates. The first step will always be to translate the argument using propositional …

## What rules of inference are used in this famous argument? “All men are mortal. Socrates is a man. Therefore, Socrates is mortal.”

As in the previous examples, first, we need to know the rules of inferences. In this example, you need to realize that you must use predicates instead of propositional variables. Because of that, we also need the rules of inference for quantified statements. Let’s use predicates to represent the argument, then we will apply the …

## Use rules of inference to show that the hypotheses “Randy works hard,” “If Randy works hard, then he is a dull boy,” and “If Randy is a dull boy, then he will not get the job” imply the conclusion “Randy will not get the job.”

To solve exercises where you have to apply rules of inference, the first step is to know the rules of inference. Once we know the rules, we can then start to apply them. So, let’s start solving the exercise. “Randy works hard,” “If Randy works hard, then he is a dull boy,” and “If Randy …

## What rule of inference is used in each of these arguments?

“Rules of inferences” is an important topic in Discrete Mathematics. We can use a rule (s) of inferences to prove if an argument is valid or not. We can also use rules of inference to produce valid arguments. In mathematics, an argument is a sequence of statements. We have a valid argument if and only …