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.

 

Understanding If-Then Statements Part 1

In this post, we are going to examine the structure and truth table of the conditional statements or if-then statements. If-then statements are used often in mathematical proofs as well as real-life conversations. But before that, let us understand what proposition means.

A proposition is a declarative sentence that is either True (T) or false (F) but not both. If-then statements are composed of two propositions.

Let us consider the following statement by a father to his son.

“If you get an A in Calculus, then I’ll buy you a laptop.”

We can split this statement into two propositions p and q as follows.  Continue reading…

 

Another Proof of the Hypotenuse Leg Theorem

Given two triangles, if their hypotenuse are congruent, and one pair of their legs are congruent then the two triangles are congruent. In this post, we are going to prove this theorem.

In the figure below, ABC and DEF are right triangles with right angles at C and F, respectively.

hypotenuse leg 1

It is given that \overline{AB} \cong \overline{DE} and \overline{AC} \cong \overline{DF}. We are going to prove that \triangle ABC \cong \triangle DEFContinue reading…