Rules of Statement and Inference

Critical reasoning is a branch of logic that deals with the analysis of arguments. When you are given a critical reasoning question in an exam, there are certain rules that you need to follow in order to arrive at the correct answer. In this blog post, we will discuss one of these rules: the rule of statement and inference. We will provide inferences examples so that you can understand how to apply this rule correctly. Let’s get started!

Critical reasoning

Critical reasoning is the process of analysing and evaluating arguments. The rules of statement and inference are a set of guidelines that help you analyse and evaluate arguments.

Inference

An inference is a logical step that is made based on the information in an argument. There are three types of inferences:

• Deductive inference: an inference that is drawn from a general principle to a specific case
• Inductive inference: an inference that is drawn from specific cases to a general principle
• Abductive inference: an inference that is drawn from the evidence to the most likely explanation

Statement

A statement is a sentence that is either true or false. The truth value of a statement can be determined by examining the evidence. Statements can be divided into two categories: propositions and declarative.

A proposition is a statement that is either true or false but cannot be verified by evidence. For example, the statement “The moon is a planet” is a proposition because it cannot be verified by evidence. However, the statement “The moon orbits around Earth” is a declarative sentence because it can be verified by evidence.

A declarative sentence is a statement that is either true or false and can be verified by evidence.

Inference rules to solve critical reasoning questions

The critical reasoning questions in statement and inference are a set of questions that test your ability to identify the logical relationships between statements. There are three main inference rules:

• Modus Ponens: This rule states that if a statement is true and I know that it is true, then I can logically infer that another statement is also true. For example, if I know that it is raining and that the ground is wet, then I can infer that it rained recently
• Modus Tollens: This rule states that if a statement is false and I know that it is false, then I can logically infer that another statement is also false. For example, if I know that it is not raining and the ground is wet, then I can infer that it did not rain recently
• Hypothetical Syllogism: This rule states that if I know that two statements are both true, then I can logically infer the third statement. For example, if I know that both it is raining and the ground is wet, then I can infer that the ground will be wet tomorrow

Let’s look at inferences examples to see how this rule works.

Example #01:

If it is raining, then the ground is wet.

P implies Q.

Therefore, Q is true.

In this example, premise P is “it is raining” and premise Q is “the ground is wet”. We know that P implies Q, so we can infer that Q is true.

Example #02:

All dogs are mammals.

P implies Q.

Therefore, Q is true.

In this example, premise P is “all dogs are mammals” and premise Q is “mammals are animals”. We know that P implies Q, so we can infer that Q is true.

Example #03:

If it is raining, then the ground is wet.

P implies Q.

Therefore, if it is not raining, then the ground is not wet.

In this example, premise P is “it is raining” and premise Q is “the ground is wet”. We know that P implies Q, so we can infer that if it is not raining, then the ground is not wet.

Conclusion

In critical reasoning questions, the rules of statement and inference are important tools to use in order to draw logical conclusions. By understanding these rules, you can quickly and easily identify valid inferences in arguments. In this guide, we have examined the two most important rules of statement and inference. We have also looked at some examples of how these rules can be applied.