Answer the following questions about rational and irrational numbers. Provide complete proofs or justifications.
a. (i) Prove that if x is an irrational number, then x+5 is irrational.
b. (ii) Prove that if x is an irrational number, then 2x is irrational.
c. (iii) Using your results from parts (i) and (ii), determine whether 32−4 is rational or irrational, and justify your conclusion.