## Thinking Mathematically (6th Edition)

An argument consists of two parts which are called the premises and a conclusion. An argument is called valid argument if conclusion is true whenever the premises are assumed to be true. Consider the simple statements in the argument with a letter: $p$: I am sick. $q$: I am tired. Express the premises and the conclusion symbolically as I am sick or I am tired: $p\vee q$ $\frac{\text{ I am not tired}}{\therefore \text{I am sick}\text{.}}$: $\frac{\tilde{\ }q}{\therefore p}$ Write a symbolic statement of the following form: $\left[ \left( \text{premise}\ \text{1} \right)\wedge \left( \text{premise}\ \text{2} \right) \right]\to \text{conclusion}$ The symbolic statement is $\left( p\vee q \right)\wedge \left( \tilde{\ }q \right)\to p$