Question

Problem 2.1 Which of the following are sets? Assume that a proper universal set has been chosen and answer by listing the names of the collections of objects that are sets. Warning: at least one of these items has an answer that, while likely, is not 100% certain. (i) A = {2,3,5,7,11,13,19} (ii) B={A,E,I,O,U} (iii) C={√x : x < 0} (iv) D = {1,2,A,5,B,Q,1,V} (v) E is the list of first names of people in the 1972 phone book in Lawrence Kansas in the order they appear in the book. There were more than 35,000 people in Lawrence that year. (vi) F is a list of the weight, to the nearest kilogram, of all people that were in Canada at any time in 2007. (vii) G is a list of all weights, to the nearest kilogram, that at least one person in Canada had in 2007.

Answer 1

Properties of sets:

A set is a collection that contains no duplicate elements.

A set can be an empty set (null set) denoted by .

(i) The set   is a valid set.

(ii)The set    is a valid set.

(iii) The set . Since , the set is the null set or set of complex numbers.

So is a valid set.

(iv) The set    is not a valid set since it cotains duplicate elements.

(v) The set

The set may not be valid since it may contain duplicate elements.

(vi) The set   is a list of the weight, to the nearest kilogram, of all people that were in Canada at any time in 2007.

The set may not be valid since it may contain duplicate elements.

vii) The set   is a list of all weights, to the nearest kilogram, that at least one person in Canada had in 2007. is a valid set since it contains no duplicate elements.