# Rules of inference

## For each of these arguments determine whether the argument is correct or incorrect and explain why

To determine whether an argument is valid or not, we should prove that it is impossible that all the premises are true and the conclusion is false. The way we do that proof is by applying one or more rules of inference on the premises and obtaining the conclusion. Like in other exercises, it is […]

## For each of these arguments, explain which rules of inference are used for each step

Like in other exercises related to rules of inferences, you first should know the basic rules of inferences before you can apply them to draw conclusions from certain premises. If you still don’t know the rules of inference, make sure you open your textbook and have rules at hand so you can apply them. Notice

## 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