Set Identities Flashcards

Questions and Answers

What does the Distributive Laws state for all sets A, B, and C?

A inter (B U C) = (A inter B) U (A inter C) (correct)

A inter C = A U B

A U B = A inter C

A U (B inter C) = (A U B) inter (A U C) (correct)

What is the Identity Law for sets A?

A inter 0 = 0

A U A = A

A U 0 = A (correct)

A inter UNIVERSAL = A (correct)

What does the Complement Laws state?

A inter A^c = 0 (correct)

A U A^c = Univ (correct)

A U A = A

A inter 0 = 0

What is the Double Complement Law for all sets A?

(A^c)^c = A Signup and view all the answers

Which of the following are true according to Idempotent Laws for all sets A?

A inter A = A Signup and view all the answers

What do Universal Bound Laws state for all sets A?

A U Univ = Univ Signup and view all the answers

What is stated by De Morgan's Laws for sets A and B?

(A U B)^c = A^c inter B^c Signup and view all the answers

What do the Absorption Laws state for all sets A and B?

A U (A inter B) = A Signup and view all the answers

What does the Set Difference Law state for sets A and B?

A - B = A inter B^c Signup and view all the answers

Study Notes

Distributive Laws

For sets A, B, and C, the laws govern the distribution of union and intersection.
First Law: A U (B ∩ C) = (A U B) ∩ (A U C)
Second Law: A ∩ (B U C) = (A ∩ B) U (A ∩ C)

Identity Laws

Identity laws clarify the effect of specific set operations.
First Law: A U Ø = A, where Ø represents the empty set.
Second Law: A ∩ UNIVERSAL = A, where UNIVERSAL refers to the universal set.

Complement Laws

Define the relationships between a set and its complement.
First Law: A U A^c = UNIVERSAL, where A^c is the complement of A.
Second Law: A ∩ A^c = Ø, indicating that a set and its complement have no elements in common.

Double Complement Law

States that taking the complement twice returns the original set.
(A^c)^c = A

Idempotent Laws

Describes the results of union and intersection operations performed multiple times on the same set.
First Law: A U A = A
Second Law: A ∩ A = A

Universal Bound Laws

Address the interaction of any set with the universal set and the empty set.
First Law: A U UNIVERSAL = UNIVERSAL; the union with the universal set results in the universal set.
Second Law: A ∩ Ø = Ø; the intersection with the empty set yields an empty set.

De Morgan's Laws

Provides crucial insights into the relationship between set operations and their complements.
First Law: (A U B)^c = A^c ∩ B^c, representing the complement of a union.
Second Law: (A ∩ B)^c = A^c U B^c, representing the complement of an intersection.

Absorption Laws

Demonstrate how certain set operations can absorb other operations.
First Law: A U (A ∩ B) = A, indicating that the union duplicates the original set.
Second Law: A ∩ (A U B) = A, where the intersection with the union equally returns the original set.

Set Difference Law

Defines the meaning of the set difference operation.
A - B = A ∩ B^c, illustrating that the difference represents elements in A not found in B.

Description

Test your knowledge on set identities with these flashcards covering essential laws like distributive, identity, and complement laws. Perfect for students in mathematics or discrete structures. Enhance your understanding of set theory concepts and definitions!