# Set Theory - Conceptual Questions

This problem is to be considered as a tree diagram.

Directions: Consider below the branching tree diagram based on the number per 3000 American adults.

1500 Americans who 635 Democrats 293 mens

like classical music 342 women

per 3000 adults

511 Republican 260 men

251 women

354 Independents 145 men

209 women

Let T = the set of Amrican who like classical music

R = the set of Republican who like classical music

D = the set of Democrats who like classical music

I = the set of Independents who like classical music

Determine whether the statement is true or false. Justify your answer.

1. I is a member of T

2. R is a proper subset of T

3.Let M = the set of Independent men who like classical music

W = the set of Independent women who like classical music

W is a proper subset of T

4.Let M = the set of Republican men who like classical music

W = the set of Republican women who like classical music

If x is a member R, then x is a member of M.

5.Let M = the set of Republican men who like classical music

W = the set of Republican women who like classical music

If x is a member W , then x is a member of R

6.If x is a member of I, then x is not a member R

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#### Solution Preview

Assuming that all the 3000 adults that were surveyed were American ...

(1) True [Because all Independents are also American]

(2) True ...

#### Solution Summary

True/False answers with reasoning provided.