Example.
The following argument form is valid:
p →q
q →r
∴ p →r
Many arguments in mathematics contain chains of if-then statements. From the fact that one statement implies a second and the second implies a third, you can conclude that the first statement implies the third. Here is an example:
If 18,486 is divisible by 18, then 18,486 is divisible by 9.
If 18,486 is divisible by 9, then the sum of the digits of 18,486 is divisible by 9.
∴ If 18,486 is divisible by 18, then the sum of the digits of 18,486 is divisible by 9.
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