Answer to Question #138759 in Algebra for Cameron Foster

Question

1. Please represent the following using Venn Diagrams.
(a) (B ∪ C) ∩ A
(b) (B ∩ C)' ∩ A
(c) (A ∪ B) ∩ (A ∪ C)
(d) (A ∪ B)'− C

Answer 1

Explanations & Calculations

• Step by step to the final Venn diagram
• Last diagram in each row is the answer to the questioned set combination.
• All diagrams before it show the way of selecting component regions of the final one.
• Refer to them with the set-notation written below them.
• They are shown just to get an understanding how to arrive at the final solution

1)

$\qquad\qquad\qquad\small (B \cup C) \to(B \cup C)\text{with}\,A \to\to\to \bold{ (B \cup C) \cap A}$

2)

• $\qquad\qquad \small (B \cap C)^{'} \to (B \cap C)^{'} \text {with} \, A \to\to\to \bold{ (B \cap C)^{'} \cap \, A}$

3)

• $\qquad\qquad \small (A \cup B) \to (A \cup C) \to \to\to \bold{(A\cup B)\cap(A \cup C)}$

4)

• $\qquad\qquad \small (A \cup B) \to (A \cup B)^{'} \to C^{'}\to\to\to\bold{(A \cup B)^{'}-C = (A\cup B)^{'}\cap C^{'}}$