# 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 (

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

### 1 thought on “Let D = {b, a, c, k}, E = {t, a, s, k}, F = {b, a, t, h}. Using these sets, find the following: <br /> Dc ⋂ E<br /> Fc ⋂ D<br /> (”

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

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