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 About the author Eliza
[tex] \: \huge\bf\underline \red{\underline{Answer}}[/tex] 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 [tex]Dc ∩ E = \: \{ elements \: in \: E \: but \: not \: in \: D \} =\{ { t, s }\}[/tex] Fc ∩ D [tex]Fc ∩ D = \{ elements \: in \: D \: \: but \: not \: in \: F \} = \{ c, k \}[/tex] (D ⋂ E) ⋃ F [tex]( D ∩ E ) ∪ F = { a, k } ∪ F = \{ b, a, t, h, k \}[/tex] D ⋂ (E ⋃ F) [tex]D ∩ ( E ∪ F ) = D ∩ \{ t, a, s, k, b, h \} = \{ b, a, t, h \}[/tex] (F ⋂ E)c ⋂ D [tex]( F ∩ E )c ∩ D = \{ t, a \}c ∩ D =\{ b, c, k \}[/tex] (D ⋃ E)c ⋂ F [tex]( D ∪ E )c ∩ F = \{ b, a, c, k, t, s\}c ∩ F = \{ b, a, t \}[/tex] Reply
[tex] \: \huge\bf\underline \red{\underline{Answer}}[/tex]
Given:–
To Find:–
Solution:–
[tex]Dc ∩ E = \: \{ elements \: in \: E \: but \: not \: in \: D \} =\{ { t, s }\}[/tex]
[tex]Fc ∩ D = \{ elements \: in \: D \: \: but \: not \: in \: F \} = \{ c, k \}[/tex]
[tex]( D ∩ E ) ∪ F = { a, k } ∪ F = \{ b, a, t, h, k \}[/tex]
[tex]D ∩ ( E ∪ F ) = D ∩ \{ t, a, s, k, b, h \} = \{ b, a, t, h \}[/tex]
[tex]( F ∩ E )c ∩ D = \{ t, a \}c ∩ D =\{ b, c, k \}[/tex]
[tex]( D ∪ E )c ∩ F = \{ b, a, c, k, t, s\}c ∩ F = \{ b, a, t \}[/tex]