#### Answer

(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.