Question

What is demorgan's theorems explain with an example?

Answer 1

thecomplementof the union of two sets isthe same as the intersection of their complements; andthe complement of the intersection of two sets is the same as the union of their complements.In set theory andBoolean algebra, these are written formally as

Answer 2

In propositional logic and boolean algebra Demogan's law is a pair of transformation rules that are both valid rules of inference.
Ex - Think of a question like this
Let U = (1,3,5,7,9,2,4,6,8,10), A = (3,2,7,5,8,9), B = (2,5,4,8,10)
Proof Demogan's law in intersection here.
Soln.
Here, A = (3,2,7,5,8,9)
B = (2,5,4,8,10)
A ^ B = (2,5,8)
A' = (1,4,6,10)
B' = (1,3,6,7,9)
According to Demogan's law of intersection (X U Y') = X' ^ Y'
Left hand side = A ^ B
= (2,5,8)
= (1,3, 4,6,7,9,10) [1]
Right hand side = A' U B'
= (1,4,6,10)' U (1,3,6,7,9)
= (1,3,4,6,7,9,10) [2]
From the above equation [1] and [2]
We get that
Left hand side = Right hand side
SO,
(A ^ B)' = A' U B'
Hence, it is proved


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