What is ‘propositional logic’?

The world is filled with logic puzzles, whether they are the kind of puzzles you might complete in your free time, such as Sudoku, or whether they are puzzles in the context of business or work which might have an impact on your customers or on society.

For example, consider the following puzzle:

Freddy wants to celebrate his birthday with as many of his five friends as possible. His friends names are Anne, Bernie, Christine, Darius and Eve. He knows that:

• Eve is only coming if Christine and Darius are coming.
• On the other hand, Christine is only coming if Anne is also coming.
• Darius will definitely not come if both Bernie and Eve are coming to the party.
• In addition, Anne is only coming if Bernie or Christine are there.
• But if both Bernie and Anne are at the party, Eve will certainly not come.

How many of Freddy’s friend are going to his party in the best case?

We can use propositional logic to describe this problem and answer it. We will work towards answering this type of puzzle in this activity, and we will return to this specific example later.

What is propositional logic?

Propositional logic is a branch of mathematics that deals with the study of logical statements, sometimes called propositions. In simpler terms, propositional logic is a way of using symbols and logical rules to analyse and understand the structure of arguments. By argument we mean a sequence of logical statements that follow on from each other.

Propositional logic is used in many fields, including mathematics, computer science and philosophy. By studying propositional logic, you can learn how to analyse arguments and identify their logical structure. This can be a useful skill in many different areas of life as well, from making informed decisions to evaluating the arguments of others.

What is a proposition?

To understand propositional logic, it is important to first understand what a proposition is.

A proposition is a statement that is either true or false, but not both. For example, “The sky is blue” is a proposition because it can be either true or false, depending on whether the sky is indeed blue or not. However, “Are you okay?” is not a proposition because the statement doesn’t have a true or false value.

When trying to decide if a statement is a proposition, ask yourself “Does it make sense to say the statement is true, or false?”

Symbols

In propositional logic, we use symbols to represent words and propositions. You will see a lot of symbols as the course progresses, and you will see that propositional logic is represented as formulae.

Let’s get started with a couple of fundamental symbols for the terms we’ve used so far: (T) to represent true, and (F) to represent false.

In the next steps, we will look at other symbols we can use to help us create clear and logical propositions.