Statement Form/Examples/Arbitrary Example 8

Example of Statement Form

If $y$ is an integer then $z$ is not real, provided that $x$ is a rational number

has the statement form

$A \implies \paren {B \implies \neg C}$

where:

$A$ stands for $x$ is a rational number

$B$ stands for $y$ is an integer.

$C$ stands for $z$ is real.

Sources

• 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives: Exercises $1 \ \text {(h)}$