Intersection and Union of Sets
Answer:
[tex]A \cup B = \{ a, b, c, d, e \}[/tex]
[tex]B \cap C = \{ d, e \}[/tex]
[tex]A \cup C = \{ a, b, c, d, e, f \}[/tex]
Step-by-step explanation:
Given:
[tex]A = \{ a, b, c, d \}[/tex]
[tex]B = \{ b, d, e \}[/tex]
[tex]C = \{ d, e, f \}[/tex]
The Union ([tex]\cup[/tex]) of sets [tex]A[/tex] and [tex]B[/tex] is just a set containing all the elements of sets [tex]A[/tex] and [tex]B[/tex]. However, elements that are present in both sets should not repeat in the Union of Sets as the elements of a set should distinct be from each other.
Part i:
[tex]A \cup B \\ \{ a, b, c, d \} \cup \{ b, d, e \} \\ \{ a, b, c, d, e \}[/tex]
The Intersection ([tex]\cap[/tex]) of sets [tex]A[/tex] and [tex]B[/tex] is just a set containing all the elements that are both present in sets [tex]A[/tex] and [tex]B[/tex].
Part ii:
[tex]B \cap C \\ \{ b, d, e \} \cap \{ d, e, f \} \\ \{ d, e \}[/tex]
Part iii:
[tex]A \cup C \\ \{ a, b, c, d, \} \cup \{d, e, f \} \\ \{ a, b, c, d, e, f \}[/tex]
