Answer to Question #137981 in Algebra for Cameron Foster

Question

1. Please use the sets below to find the following (3pts each)
U = {a, b, c, d, e, f, g, h}
A = {a, b, c, d}
B = {c, e, g}
C = {d, e, f, g, h}

(a) A ∪ (B ∩ C)
(b) B ∪ C
(c) (B ∪ C)'
(d) A − (B ∪ C)
(e) (B ∪ C) − A

Answer 1

We are given:

$U = \{ a, b, c, d, e, f, g, h \}$

$A = \{ a, b, c, d \}$

$B = \{ c, e, g \}$

$C = \{ d, e, f, g, h \}$

Now:

$B \cup C = \{ c,e,g \} \cup \{ d, e, f, g, h \}$

$\hspace{1 cm} \, = \{ c, d, e, f, g, h \}$

And:

$B \cap C = \{ c,e,g \} \cap \{ d, e, f, g, h \}$

$\hspace{1 cm} \, = \{ e, g \}$

a.)

$A \cup \left( B \cap C \right) = \{ a,b, c, d \} \cup \{ e, g \}$

$\hspace{1 cm}\hspace{0.9 cm} \, = \{ a, b, c, d, e, g \}$

b.)

$B \cup C = \{ c,e,g \} \cup \{ d, e, f, g, h \}$

$\hspace{1 cm} \, = \{ c, d, e, f, g, h \}$

c.)

$\left( B \cup C \right)^{'} = U - \left( B \cup C \right)$

$\hspace{1 cm} \hspace{0.4 cm} = \{ a, b, c, d, e, f, g, h \} - \{ c, d, e, f, g, h \}$

$\hspace{1 cm} \hspace{0.4 cm} = \{ a, b \}$

d.)

$A - \left( B \cup C \right) = \{ a, b, c, d \} - \{ c, d, e, f, g, h \}$

$\hspace{1 cm} \hspace{1 cm} = \{ a, b \}$

e.)

$\left( B \cup C \right) - A = \{ c, d, e, f, g, h \} - \{ a, b, c, d \}$

$\hspace{1 cm} \hspace{1 cm} = \{ e, f, g, h \}$