Answer to Question #148954 in Statistics and Probability for Mani

Question

The following sets are used in a company's database:
Workforce = {Abi, Baz, Cal, Dev, Eva, Fay, Ged}
Department = { Accounts, Operations, Research, Sales}
Place = {Sheffield, Leeds, London}
ProjectTeams = {A, B, C}
A = {Abi, Eva, Fay}
B = {Baz, Dev, Eva, Fay}
C = {Cal, Eva, Ged}
Find the following:
(a) A ∩ B
(b) B ∪ C
(c) A ∩ B ∩ C
(d) Workforce \ B
(e) Workforce \ (A ∪ C)
(f) (Workforce \ B) \ C
(g) The power set P(A)
(h) The Cartesian product Place x ProjectTeams
(i) The number of elements in the power set P(Department)
(j) P(A) ∪ A

Answer 1

(a) $A\cap B=\{Eva, Fay\}$

(b) $B\cup C=\{Baz,Cal,Dev,Eva,Fed,Ged\}$

(c) $A\cap B\cap C=\{Eva\}$

(d) $Workforce \backslash B=\{Abi,Cal,Ged\}$

(e) $Workforce \backslash (A\cup C)=\{Baz,Dev\}$

(f) $(Workforce \backslash B)\backslash C =\{Abi\}$

(g) The power set $P(A)=\{\{\},\{Abi\}, \{Eva\}, \{Fay\},\{Abi,Eva\},$

$\{Abi,Fay\},\{Eva,Fay\},\{Abi,Eva,Fay\}\}$

(h) The Cartesian product Place x ProjectTeams

$=\{\{Sheffield,A\},\{Sheffield,B\},\{Sheffield,C\},$

$\{Leeds,A\},\{Leeds,B\},\{Leeds,C\},$

$\{London,A\},\{London,B\},\{London,C\}\}$

(i) The number of elements in the power set P(Department)

$$2^4=16$$

(j) $P(A)\cup A=P(A)=\{\{\},\{Abi\}, \{Eva\}, \{Fay\},$

$\{Abi,Eva\},\{Abi,Fay\},\{Eva,Fay\},$

$\{Abi,Eva,Fay\}\}$