show how to verify the demorgan's law in venn diagrams.

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(A U B)^'=A' n B'

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Arindam Phatowali answered this

First draw vann diagram for A complement and then for B compement, combine them and u will get (A U B)complement.
Follow the same for (A intersectionC).

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Nakul answered this

(A U B)' = A U B s complement because thiz ' (inverted comma mnz complement) mnz other than A U B ..... And A' inverted U (intersection) B' is same as ( A U B )' ..... which is Demorganzz law

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Proofs for De Morgan's laws :

Here we are going to see the proof of De morgan's laws by Venn diagram.

De morgan's laws

De morgan's law for set difference :

For any three sets A, B and C, we have

(i) A \ (B u C) = (A \ B) n (A \ C)

(ii) A \ (B n C) = (A \ B) u (A \ C)

De morgan's law for set complementation :

Let U be the universal set containing sets A and B. Then

(i) (A u B)' = A' n B'

(ii) (A n B)' = A' u B'

Proof by Venn diagram

A \ (B n C) = (A \ B) u (A \ C)

From the above Venn diagrams (2) and (5), it is clear that

A \ (B n C) = (A \ B) u (A \ C)

Hence, De morgan's law for set difference is verified.

Now, let us look at the Venn diagram proof of De morgan's law for complementation.

(A n B)' = A' u B'

From the above Venn diagrams (2) and (5), it is clear that

(A n B)' = A' u B'

Hence, De morgan's law for complementation is verified.

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Proofs for De Morgan's laws :

Here we are going to see the proof of De morgan's laws by Venn diagram.

De morgan's laws

De morgan's law for set difference :

For any three sets A, B and C, we have

(i) A \ (B u C) = (A \ B) n (A \ C)

(ii) A \ (B n C) = (A \ B) u (A \ C)

De morgan's law for set complementation :

Let U be the universal set containing sets A and B. Then

(i) (A u B)' = A' n B'

(ii) (A n B)' = A' u B'

Proof by Venn diagram

A \ (B n C) = (A \ B) u (A \ C)

From the above Venn diagrams (2) and (5), it is clear that

A \ (B n C) = (A \ B) u (A \ C)

Hence, De morgan's law for set difference is verified.

Now, let us look at the Venn diagram proof of De morgan's law for complementation.

(A n B)' = A' u B'

From the above Venn diagrams (2) and (5), it is clear that

(A n B)' = A' u B'

Hence, De morgan's law for complementation is verified.

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