Question

Let U = {x/x belongs to a natural number and x is less than or equal to 8} , A = {x/x , 5 < x < 50} and B = { x/x is prime } , Then Verify (De Morgan's Law)
1.) (A U B) Complement = A Complement Intersect B Complement
2.) (A Intersect B) = A Complement U B Complement
[ 11th CBSE Maths , Chapter - 1 Sets​ ]

Answer 1

SOLUTION

GIVEN

U = { x : x ∈ N and x ≤ 8 }

A = { x : 5 < x² < 50 }

B = { x : x is prime }

TO VERIFY

De Morgan's Law

(i) ( A ∪ B )' = A' ∩ B'

(ii) ( A ∩ B )' = A' ∪ B'

EVALUATION

U = { x : x ∈ N and x ≤ 8 }

= { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

A = { x : 5 < x² < 50 }

= { 3 , 4 , 5 , 6 , 7 }

B = { x : x is prime }

= { 2 , 3 , 4 , 5 , 6 , 7 }

PROOF TO QUESTION : (i)

A ∪ B = { 2 , 3 , 4 , 5 , 6 , 7 }

( A ∪ B )' = { 1 , 8 }

A' = { 1 , 2 , 8 }

B' = { 1 , 4 , 6 , 8 }

A' ∩ B' = { 1 , 8 }

∴ ( A ∪ B )' = A' ∩ B'

ANSWER TO QUESTION : (ii)

A ∩ B = { 3 , 5 , 7 }

( A ∩ B )' = { 1 , 2 , 4 , 6 , 8 }

A' = { 1 , 2 , 8 }

B' = { 1 , 4 , 6 , 8 }

A' ∪ B' = { 1 , 2 , 4 , 6 , 8 }

∴ ( A ∩ B )' = A' ∪ B'

Hence verified

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