please do all the questions!

13. Russell's Paradox shows that (a) Not all sets are finite (b) Naive set theory is inconsistent (c) R has the cardinslity of the continuum (d) There can be no set with cardinality less than N 14. If ABA=B then (a) A and B are countable (b) B is finite (c) B is infinite (d) A is finite 15. A for every set A can be proven by (a) vacuity (b) cases (c) existence (d) contradiction 16. The following set is countable (a) R (b) [0,1] (all real numbers between 0 and 1 ) (c) 2N (d) {1,2,3}