Prove the DeMorgan Law:
A^CUB^C
DeMorgan Law Identity
(A ∩ B)C = AC U BC
Define x
Let x be an element of (A ∩ B)C, x ∈ (A ∩ B)C
Simplify
x ∉ (A ∩ B)
x ∉ A or x ∉ B
x ∈ AC or x ∈ BC
x ∈ AC U BC
What is the Answer?
x ∈ AC U BC
How does the DeMorgans Laws Calculator work?
Free DeMorgans Laws Calculator - Demonstrates DeMorgans Laws including the proof
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This calculator has 1 input.
What 2 formulas are used for the DeMorgans Laws Calculator?
(A U B)C = A‘ ∩ B‘
(A ∩ B)‘ = A‘ U B‘
(A ∩ B)‘ = A‘ U B‘
What 9 concepts are covered in the DeMorgans Laws Calculator?
- complement
- The opposite of an event happening
AC - demorgans laws
- element
- an element (or member) of a set is any one of the distinct objects that belong to that set. In chemistry, any substance that cannot be decomposed into simpler substances by ordinary chemical processes.
- intersection
- the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A.
A ∩ B - law
- a mathematical statement which always holds true
- notation
- An expression made up of symbols for representing operations, unspecified numbers, relations and any other mathematical objects
- proof
- an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
- set
- a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
- union
- Combine the elements of two or more sets
