# Venn Diagram

• Oct 22nd 2005, 04:19 AM
alexis
Right then who can do this tuff cookie (1)
1. By drawing a Venn Diagrams with three overlapping circles show that generally (AUB)nC not equal to AU(BnC)

What are the conditions on A, B and C for (AUB)nC equal to AU(BnC)

If A = {irrationals}, B = {integers} and C {reals} does the equality from above hold in this case? Draw a Venn Diagram showing the relationships between A, B and C?
• Oct 23rd 2005, 05:52 AM
hpe
Quote:

Originally Posted by alexis
1. By drawing a Venn Diagrams with three overlapping circles show that generally (AUB)nC not equal to AU(BnC)

What are the conditions on A, B and C for (AUB)nC equal to AU(BnC)

If A = {irrationals}, B = {integers} and C {reals} does the equality from above hold in this case? Draw a Venn Diagram showing the relationships between A, B and C?

Since \$\displaystyle (A \cup B) \cap C = (A \cap C) \cup (B \cap C)\$, the condition is that \$\displaystyle A = A \cap C \$ or equivalently \$\displaystyle A \subset C \$. In the case described by you, the condition is true.