Answer to Question #328298 in Discrete Mathematics for Grewishker

Question

a. Determine the sets A and B, if A − B = {1, 2, 7, 8}, B − A = {3, 4, 10} and A ∩ B

= {5, 6, 9}.

b. Verify A ∪ (A ∩ B) = A using the rules of set algebra

Answer 1

a.

$A = (A - B) \cup A \cap B = \{ 1,2,7,8\} \cup \{ 5,6,9\} = \{ 1,2,5,6,7,8,9\}$

$B = (B - A) \cup A \cap B = \{ 3,4,10\} \cup \{ 5,6,9\} = \{ 3,4,5,6,9,10\}$

b. $A \cup \left( {A \cap B} \right) = \{ {\rm{ }}1,2,5,6,7,8,9\} \cup \{ 5,6,9\} = \{ {\rm{ }}1,2,5,6,7,8,9\} = A$

Q.E.D.