Question

Let D = {b, a, c, k}, E = {t, a, s, k}, F = {b, a, t, h}. Using these sets, find the following:
Dc ⋂ E
Fc ⋂ D
(D ⋂ E) ⋃ F
D ⋂ (E ⋃ F)
(F ⋂ E)c ⋂ D
(D ⋃ E)c ⋂ F

Answer 1

$\: \huge\bf\underline \red{\underline{Answer}}$

Given:-

• D = {b, a, c, k}
• E = {t, a, s, k}
• F = {b, a, t, h}

To Find:-

• Dc ⋂ E
• Fc ⋂ D
• (D ⋂ E) ⋃ F
• D ⋂ (E ⋃ F)
• (F ⋂ E)c ⋂ D
• (D ⋃ E)c ⋂ F

Solution:-

• Dc ⋂ E

$Dc ∩ E = \: \{ elements \: in \: E \: but \: not \: in \: D \} =\{ { t, s }\}$

• Fc ∩ D

$Fc ∩ D = \{ elements \: in \: D \: \: but \: not \: in \: F \} = \{ c, k \}$

• (D ⋂ E) ⋃ F

$( D ∩ E ) ∪ F = { a, k } ∪ F = \{ b, a, t, h, k \}$

• D ⋂ (E ⋃ F)

$D ∩ ( E ∪ F ) = D ∩ \{ t, a, s, k, b, h \} = \{ b, a, t, h \}$

• (F ⋂ E)c ⋂ D

$( F ∩ E )c ∩ D = \{ t, a \}c ∩ D =\{ b, c, k \}$

• (D ⋃ E)c ⋂ F

$( D ∪ E )c ∩ F = \{ b, a, c, k, t, s\}c ∩ F = \{ b, a, t \}$