6. [8 POINTS) Letbe a nonzero real number. Prove by way of contrapositive that if x+…

6. [8 POINTS) Letbe a nonzero real number. Prove by way of contrapositive that if x+ irrational, then is irrational. is 7. 18 POINTS Consider a collection of closed intervals ( hal. = 1.2.3…. such that lim(b,- ) = 0 Prove by way of contradiction that there cannot be more than one real number contained in each of these intervals.