Decide whether each statement is true or false.a) {2, 4, 6, 8, c} ⊆ {1, 2, 3, 4, c}b) In t...

Decide whether each statement is true or false.

a) {2, 4, 6, 8, c} ⊆ {1, 2, 3, 4, c}

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b) In the table in Example T ⊆ A.

Example Identifying Subsets

Consider the following table regarding medalists in the 2008 Summer Olympic Games in Beijing, China.

Assume that this set is the universal set, and define the following sets:

T = the set of trampoline medalists

A = the set of U.S. athletes

G = the set of gold medal winners

Which statements are true?

a) A ⊆ G

b) A ⊆ G

c) T ⊆ G

SOLUTION:

a) This is true because every element of A, which equals the set {Liukin, Peirsol}, is also an element of the set G = {Wenna, Liukin, Majewski, Izbasa, Peirsol}.

b) This is also true. We already know that A ⊆ G. Because G contains an element that is not in A–for example, Majewski–this means that A is a proper subset of G.

c) This is false. Set T has an element, Khilko, that is not an element of G.