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 q.
In the definition above, simple propositions mean propositions that cannot be broken down further into simpler propositions.
Notice that in the definition above, we added not, another logical connector. This connector does not connect two propositions. Below are some examples of compound propositions.
1.) It is not the case that square root of 2 is a rational number.
2.) I’ll go mountain climbing or fishing this weekend.
3.) Either math is fun and interesting, or it is boring.
4.) These stuff toys are soft and fluffy.
5.) You are going to have biscuits or cookies for snacks.
6.) It will rain today and it will rain tomorrow.
7.) It is sunny and it is humid.
8.) If I pass the exam, I’ll take you out for dinner.
9.) If you study hard, then you will get good marks.
10.) If n is an integer, then n is even or n is odd.
Since these are propositions, they are either true or false. Now, how do we determine the truth values of compound propositions? We will discuss this one by one in the next post.