Answer
The argument is true by Elimination
Work Step by Step
Let p be the statement that This real number is rational.
Let q be the statement that This real number is irrational.
This real number is rational or it is irrational (p ∨ q)
This real number is not rational (¬p)
∴ This real number is irrational (q)
So the argument form is:
p ∨ q
¬p
∴ q
Which is true by the rule of inference known as $Elimination$
