## Thinking Mathematically (6th Edition)

Euler diagram is used for the arguments whose premises contain the words all, some, and no. Example: Consider the arguments given below. All botanists are scientists. $\text{All scientists have college degrees}\text{.}$ $\therefore \text{All botanists have college degrees}\text{.}$ The premises of the above argument contain the word all. Thus, it needs to be solved using Euler diagram instead of the truth table. But, for the arguments given below, If I am tired, I am edgy. $\text{If I am edgy, I am nasty}\text{.}$ $\therefore \text{If I am tired, I am nasty}\text{.}$ Its symbolic form is \begin{align} & p\to q \\ & q\to r \\ & \therefore p\to r \\ \end{align} By determining the truth values of $p\to q$, $p\to q$, and $p\to q$, the argument can be solved using truth table.