Algebra 04 - Complement and Relative Complement

Professor Von Schmeelk introduces the concept of set complements and relative complements using Venn diagrams. The lecture explains the definition of a set's complement, emphasizing the importance of defining a universal set. Examples are provided using integers and natural numbers. The lecture also covers the concept of relative complements, highlighting the differences from absolute complements. The session concludes with a preview of the next lecture on symmetric difference.

What is the universal set typically designated by?

• The letter R

• The letter N

• The letter U

• The letter Z

In the context of set theory, what does the complement of a set represent?

• All elements that are members of the universal set

• All elements that are members of the set

• All elements that are members of both the set and the universal set

• All elements that are not members of the set

How is the complement of a set A typically denoted?

• A with a prime symbol

• A with a superscript C

• A with a subscript C

• A with a ball over it

What is a unary operation in the context of set theory?

• An operation involving two operands

• An operation involving only one operand

• An operation involving three operands

• An operation involving no operands

What is the relative complement of set A in set B?

• All elements in A that are not in B

• All elements in B that are not in A

• All elements in both A and B

• All elements in neither A nor B

How is the relative complement of A in B sometimes denoted?

• B backslash A

• A backslash B

• B minus A

• A minus B

What is the main difference between absolute and relative complements?

• Absolute complements require A to be a subset of B

• Relative complements require A to be a subset of B

• Absolute complements do not require a universal set

• Relative complements do not require a universal set