Let U denote the set of all senators in Congress and let D  =  {x U | x is a Democrat} R  =  {x U | x is a Republican} F  =  {x U | x is a female} P  =  {x U | x is a physician}. Write the set that represents each statement. (a) The set of all Democrats who are female or are physicians a. D ∩ (F ∩ P) b. D ∩ (F ∪ P)     c. R ∪ (F ∪ P) d. D ∪ (F ∩ P) e.R ∩ (F ∪ P) (b) The set of all senators who are not Democrats or are physicians a. Dc ∪ P b. Dc ∩ P  c. R ∩ P d. (D ∪P)c e. (D ∩ P)c

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Chapter1: Combinatorial Analysis
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Let U denote the set of all senators in Congress and let

D  =  {x U | x is a Democrat}
R  =  {x U | x is a Republican}
F  =  {x U | x is a female}
P  =  {x U | x is a physician}.

Write the set that represents each statement.

(a) The set of all Democrats who are female or are physicians
a. D ∩ (F ∩ P)
b. D ∩ (F ∪ P)    
c. R ∪ (F ∪ P)
d. D ∪ (F ∩ P)
e.R ∩ (F ∪ P)

(b) The set of all senators who are not Democrats or are physicians
a. Dc ∪ P
b. Dc ∩ P
 c. R ∩ P
d. (D ∪P)c
e. (D ∩ P)c
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