# Law of Syllogism

Math isn''t just fun -- it can also help us figure out all kinds of problems that we encounter in the real world. Although it might seem like math is just numbers on a piece of paper, the truth is the world around you is filled with all kinds of equations. If we encounter a logic problem, we can turn it into a formula. If we solve the formula, then we solve the problem, allowing us to make better, more logical decisions. This is where the Law of Syllogism comes into play.

## What is the Law of Syllogism?

The Law of Syllogism in logic helps us draw conclusions from two given conditional statements. Conditional statements can be represented as "if p, then q."

Examples include:

"If it snows tomorrow, then class will be canceled."

"If my grade is lower than 50%, then I''m going to fail."

The Law of Syllogism connects two conditional statements when the conclusion of the first statement matches the hypothesis of the second statement.

Consider these two conditional statements:

"If it snows tomorrow, then class will be canceled."

"If class is canceled tomorrow, I don''t have to study for the math test."

In this case, the conclusion of the first statement (class being canceled) matches the hypothesis of the second statement. According to the Law of Syllogism, we can now create a new conditional statement that connects the hypothesis of the first statement with the conclusion of the second statement:

"If it snows tomorrow, I don''t have to study for the math test."

So, we can see that the Law of Syllogism allows us to draw a conclusion by connecting the hypothesis of the first statement (p) with the conclusion of the second statement (r), eliminating the middle term (q) from the chain.

## Why is the Law of Syllogism important?

The Law of Syllogism is important because it is a foundational aspect of deductive reasoning, which is a key element of logical thinking and problem-solving. By connecting two related conditional statements, the Law of Syllogism allows us to reach new conclusions and simplify complex chains of reasoning.

For example, let''s consider a real-world scenario:

2. "If I receive a notification, I can pick up the package from the post office."

Using the Law of Syllogism, we can draw a new conclusion:

"If the package arrives today, I can pick up the package from the post office."

This conclusion helps us understand the implications of the package''s arrival without having to analyze both conditional statements separately.

## Topics related to the Law of Syllogism

Law of Detachment

Symbolic Logic

Converse, Inverse and Contrapositive

## Flashcards covering the Law of Syllogism

Symbolic Logic Flashcards

Introduction to Proofs Flashcards

## Practice tests covering the Law of Syllogism

Introduction to Proofs Practice Tests

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