let A and B be two sets then (A U B)' U(A' ∩ B) is equal to
Answers
Union means addition of all the elements of both the sets.
Intersection means common elements of both the sets.
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Since AUB=A
It indicates B is a empty set or have same elements which set A have because at union fuction also the answer is A.
So it it conclude that if set B is null set then
A∩B=A
and if set B have same element that set A have then
A∩B=A or A∩B=B.
Answer:
The value of (AUB)'U(A'∩B) = A'
Step-by-step explanation:
De-Morgan's Law:
De - Morgan's First law:
It states that the complement of the union of two sets is the intersection of their complements.
(AUB)' = A'∩B'
De - Morgan's Second Law:
It states that the complement of the intersection of two sets is the union of their complements.
(A∩B)' = A'UB'
These two laws are called De Morgan's Law.
Let S = (AUB)'U(A'∩B)
According to De - Morgan's law, (AUB)' = A'∩B'
S = (A'∩B')U(A'∩B)
= (A'UA')∩(A'UB)∩(B'UA')∩(B'UB)
= A' ∩ {AU(B∩B')} ∩ U
where U is the universal set
S = A' ∩ (A'∪ ∅) ∩ U
= A' ∩ A' ∩ U
= A' ∩ U
S = A'
Hence (AUB)'U(A'∩B) = A'
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