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Status: Tags: Links: Discrete Mathematics

Set Operations

Operations can be expressed visually through Set Venn Diagrams

Logics vs Sets

Set Notation

Complements

Set that comprises all elements of U that do not belong to A !Complement Set.excalidraw

Intersections

? !Drawing 2021-07-06 14.51.58.excalidraw Ex)

• {1,3,5,7} ∩ {2,3,4,5,6} = {3,5}

Unions

? Ex)

• {1,3,5,7} ∪ {2,3,4,5,6} = {1,2,3,4,5,6,7}

Differences

? Include elements of A if not in B Ex)

• {1,3,5} - {1,2,3} = {5}

Symmetric Differences

? A∆B=(A-B) ∪(B-A)

Cool Proofe

Disjoint Sets

? A ∩ B = ∅

Principle of Inclusion-Exclusion

?

Proofs

ExamplesOfProofs.DVI (washington.edu)

Steps for proving equivalence a = b

?

• Prove that a implies b and b implies a
• Start with a, and manipulate to turn into b using definitions
• Start with b, manipulate to turn into a using definitions
• Thus, a = b

Prove $A - B = A n B^c$

?

Sets A and B are disjoint if and only if A ∪ B = A ∆ B

? Proof

DeMorgan’s Law in Set Notation

DeMorgan’s Law using set builder and logic

Backlinks

1

list from Set Operations

References:

Created:: 2021-07-06 14:07