Question: 4. (a) Provide an example of sets E, 31, 5'2 and 33 such that (i) E31S253Q; (ii) E has a least upper bound in 31,

4. (a) Provide an example of sets E, 31, 5'2 and 33 such that (i) E31S253Q; (ii) E has a least upper bound in 31, (iii) E does not have a least upper bound in 8'2, and (iv) E has a least upper bound in 33. (b) Prove that for any sets E, 81, 82 and S3 satisfying properties (i)(iv) of part (a), the least upper bound of E in 51 does not equal the least upper bound of E in 5'3. (0) Prove or disprove: There exist sets E, 5'1, 82 and 33 satisfying properties (i)*(iv) of part (a) such that E = 81

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