## Thinking Mathematically (6th Edition)

(a) The statement is “Smoking reduces life expectancy by 2370 days, and heart disease reduces life expectancy by 1247 days.” By using the following representation in statement, $p:$Smoking reduces life expectancy by 2370 days. $q:$Heart disease reduces life expectancy by 1247 days. The symbolic form of the statement is$p\wedge q$. From the graph, it can be seen that p is true and q is false. Hence, put the truth values of p and q in symbolical statement as $\text{T}\wedge \left( \sim \text{T} \right)\equiv \text{T}\wedge \text{F}\equiv \text{F}$ It implies that the provided statement is false. (b) By using the following representation in statement, $p:$Smoking reduces life expectancy by 2370 days. $q:$Heart disease reduces life expectancy by 1247 days. The symbolic form of the statement is $p\wedge q$. Negation of $p\wedge q$is $\sim p\vee \sim q$. By using p and q, the statement form of $\sim p\vee \sim q$ is “Smoking does not reduce life expectancy by 2370 days or heart disease does not reduce life expectancy by 1247 days.” (c) By using the following representation in statement, $p:$Smoking reduces life expectancy by 2370 days. $q:$ Heart disease reduces life expectancy by 1247 days. The symbolic form of the statement is$\sim p\vee \sim q$. From the provided graph, it can be seen that p is true and q is false. Hence, put the truth values of p and q in symbolical statement as $F\wedge T\equiv T$ It implies that the provided statement is true.