Math Problem Solver

QUESTION 1

1.1 Given sets A and B. Define what is meant by the statement A is equivalent to B. Denote this

equivalence by . A B (1)

1.2 If A and B are finite sets show that if A B then A B = , i.e. A and B have the same

cardinality. (3)

1.3 Show 2 i.e. 1,2,3,4... 1,4,9,16,... . Does this contradict 1.2 above ? (5)

1.4 Prove that sets equivalence “ ” as defined above is indeed an equivalence relation on the

subsets of a given universal set U. That is given sets A, B, C in U then

(i) A A

(ii) A B B A

(iii) & . A B B C A C

(Hint: Only explain what mapping you use in your claim, no need to prove bijectiveness of such

mapping)