Consider the Venn diagram below. A B C U a. Illustrate one of the distributive laws by

Chapter 6, Problem 23

(choose chapter or problem)

Consider the Venn diagram below.

                                               

a. Illustrate one of the distributive laws by shading in the region corresponding to \(A \cup(B \cap C)\) on one copy of the diagram and \((A \cup B) \cap(A \cup C)\) on another.

b. Illustrate the other distributive law by shading in the region corresponding to \(A \cap(B \cup C)\) on one copy of the diagram and \((A \cap B) \cup(A \cap C)\) on another.

c. Illustrate one of De Morgan’s laws by shading in the region corresponding to \((A \cup B)^{c}\) on one copy of the diagram and \(A^{c} \cap B^{c}\) on the other. (Leave the set C out of your diagrams.)

d. Illustrate the other De Morgan’s law by shading in the region corresponding to \((A \cap B)^{c}\) on one copy of the diagram and \(A^{c} \cup B^{c}\) on the other. (Leave the set C out of your diagrams.)

Text Transcription:

A cup(B cap C)

(A cup B) cap(A cup C)

A cap(B cup C)

(A cap B) cup(A cap C)

(A cup B)^c

A^c cap B^c

(A cap B)^c

A^c cup B^c