Question

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10), A=(2, 4, 6, 8, 10), B = (1, 3, 5, 7, 9) and C= (1, 2, 3, 4, 5) Using properties of sets, show that AU (An B) = A and An (AUB) = A.​

Answer 1

Step-by-step explanation:

Given :-

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A={2, 4, 6, 8, 10}

B = {1, 3, 5, 7, 9}

C= {1, 2, 3, 4, 5}

To find :-

Show that AU (An B) = A and An (AUB) = A.

Solution :-

Given sets are :-

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A={2, 4, 6, 8, 10}

B = {1, 3, 5, 7, 9 }

C= {1, 2, 3, 4, 5}

i) AU (An B) = A :-

AnB = { 2, 4, 6, 8, 10} n {1, 3, 5, 7, 9}

=> AnB = { }

Now,

AU (AnB) = { 2, 4, 6, 8, 10} U { }

=> AU (AnB) = { 2, 4, 6, 8, 10}

=> AU (AnB) = A

ii)An (AUB) = A:-

AUB = { 2, 4, 6, 8, 10} U {1, 3, 5, 7, 9}

=> AUB = { 1,2,3,4,5,6,7,8,9,10}

Now,

An (AUB) = { 2, 4, 6, 8, 10} n { 1,2,3,4,5,6,7,8,9,10}

=> An(AUB) = { 2, 4, 6, 8, 10}

=> An (AUB) = A

Hence, Proved.

Answer:-

i)AU (An B) = A

ii) An (AUB) = A.

Used formulae:-

→The set of all elements in either A or in B or in both is called the Union of the sets A and B . It is denoted by AUB.

→The set of all common elements in both A and B is called Intersection of the sets A and B . It is denoted by AnB.

Answer 2

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