Introduction to Compound Propositions

In the previous post, we have learned about propositions. We learned that propositions are statements that are either true or false but not both. In this post, we are going to combine two or more propositions using words such as and, or, and if and then. Two or more propositions combined are called compound propositions and the words used to combined them are called logical connectors. We formalize our knowledge about compound propositions by the following definition.


A compound proposition is a proposition formed from simpler propositions using logical connectors or some combination of logical connectors. Some logical connectors involving propositions p and/or q may be expressed as follows: not p, p and q, p or q, if p then qContinue reading…


Understanding Propositions

In the previous post, I have promised that we will take our discussion about mathematical proofs to the next level. We will start this journey by learning about propositions.

In our daily lives, we often encounter statements that are either true or false. Some examples are shown below.

1.) Australia is an island continent.
2.) The Earth revolves around the sun.
3.) Asia is the largest continent.
4.) The sum of 3 and 5 is 9.
5.) The Earth has two moons.

As we can see, the first three statements above are true while the last two statements are false.

Statements that are either true or false, but not both are called propositions. If a proposition is true, then its truth value is True (usually denoted by T) and if it is false, its truth value is False (usually denoted by F). Another characteristic of a proposition is it is a declarative sentence. Therefore, to check if a statement is a proposition or not,  you have to check if  (1) it is a declarative sentence and (2) it is either true or false.  Continue reading…


A reboot for Proofs from the Book

I have decided to include undergraduate proofs in this blog. We will be studying formal proofs starting with logic (truth tables, logical connectives, etc.) and then study different methods of proofs (direct, indirect, etc).

While studying these concepts, we will have numerous examples from different branches of mathematics particularly number theory, probability, and combinatorics.

I’m very excited to start this series, so just keep posted.