If A and B be any two sets, then (A∪B)‘ is equal toa)A′∪B′b)A∪Bc)A∩Bd)A′∩B′Correct answer is option 'D'. Can you explain this answer?

Question

If A and B be any two sets, then (A&#8746;B)&#8216; is equal toa)A&#8242;&#8746;B&#8242;b)A&#8746;Bc)A&#8745;Bd)A&#8242;&#8745;B&#8242;Correct answer is option 'D'. Can you explain this answer?

Answer

Explanation:

- In set theory, the symbol AB represents the intersection of sets A and B, i.e. the set of all elements that belong to both A and B.
- The intersection of two sets A and B is defined as follows: AB = {x | x ∈ A and x ∈ B}.
- For example, if A = {1, 2, 3} and B = {2, 3, 4}, then AB = {2, 3}.
- The intersection of two sets A and B is also denoted by A ∩ B, where the symbol ∩ represents the intersection operation. Therefore, AB = A ∩ B.
- The intersection of two sets A and B has the following properties:

- Commutative property: AB = BA
- Associative property: (AB)C = A(BC)
- Distributive property: A(B ∪ C) = AB ∪ AC and A(B ∩ C) = AB ∩ AC

- Therefore, if A and B are any two sets, then (AB) = (A ∩ B) = (B ∩ A) = (BA) = (BA) = (AB). Hence, option D is the correct answer.

Answer

Answer

By de-morgan's law
(A U B)' = A' intersection B'

Answer

Answer

Let A ={1} and B={1 , 2 } U = {1 , 2 , 3}
so, A U B = {1} U {1 , 2} = {1 , 2}
therefore, (A U B )'= {3}
*option (a):- A' U B' = {2 , 3 } U { 3} = { 2 , 3 }
thus, option (a) is not true
*option (b):- A U B = { 1 , 2}
hence option is not correct
*option (c):- A intersection B = {1} intersection {1,2} = {1}
hence option is not correct
*option (d):- A' intersection B' = {2,3} intersection {3}={3}
therefore (A U B )' = A' intersection B'

Answer

Let A ={1} and B={1 , 2 } U = {1 , 2 , 3}
so, A U B = {1} U {1 , 2} = {1 , 2}
therefore, (A U B )'= {3}
*option (a):- A' U B' = {2 , 3 } U { 3} = { 2 , 3 }
thus, option (a) is not true
*option (b):- A U B = { 1 , 2}
hence option is not correct
*option (c):- A intersection B = {1} intersection {1,2} = {1}
hence option is not correct
*option (d):- A' intersection B' = {2,3} intersection {3}={3}
therefore (A U B )' = A' intersection B'
thus option (d) is correct ans

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