Question

prove that De Morgan's law​

Answer 1

Answer:

Definition of De Morgan's law: ... The complement of the union of two sets is equal to the intersection of their complements and the complement of the intersection of two sets is equal to the union of their complements. These are called De Morgan's laws.

Answer 2

Answer:

. If U = {j, k, l, m, n}, X = {j, k, m} and Y = {k, m, n}.

Proof of De Morgan's law: (X ∩ Y)' = X' U Y'.

Solution:

We know, U = {j, k, l, m, n}

X = {j, k, m}

Y = {k, m, n}

(X ∩ Y) = {j, k, m} ∩ {k, m, n}

= {k, m}

Therefore, (X ∩ Y)' = {j, l, n} ……………….. (i)

Again, X = {j, k, m} so, X' = {l, n}

and Y = {k, m, n} so, Y' = {j, l}

X' ∪ Y' = {l, n} ∪ {j, l}

Therefore, X' ∪ Y' = {j, l, n} ……………….. (ii)

Combining (i)and (ii) we get;

(X ∩ Y)' = X' U Y'. Proved

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