Question

Which of the following set of numbers illustrates the intersection of sets A and B? A = {1,2,3,4} B = {1,3,5,7}

Answer 1

Answer:

Step-by-step explanation:

Explanation :

U = {1,2,3,4,5,6} , A={2,3} and B={3,4,5}

therefore ,

A'= {1,4,5,6}

B'={1,2,6}

A′ ∩ B′ = {1,6}

Now to show ( A ∪ B )′ = A′∩ B′ , first find ( A ∪ B )

(A U B) = {2,3,4,5,}

Now, ( A ∪ B )′ = {1,6}

As we have already know, A′ ∩ B′ = {1,6}

therefore, ( A ∪ B )′ = A′∩ B′

Additional information :

1] what is complement of set? :

consider A is the set, which is subset of the universal set U. then

the set of all those elements of U which do not belongs to A is called the complement of A with respect to U, it is denoted as A'

2]what is (AUB) [ union of sets ] ? :

if A and B are two sets, then the set of those elements which belong to A or to B or to both A and B, is called the union of the sets A and B,

it is denoted as AUB

3 ] what is intersection of sets? :

if A and B are two sets, then the set of those elements which belong to both A and B, i.e which are common to both A and B, is called the intersection of the set A and B

it is denoted by A∩B

Answer 2

SOLUTION

GIVEN

A = {1,2,3,4} , B = {1,3,5,7}

TO DETERMINE

A ∩ B

EVALUATION

Here the given sets are

A = {1,2,3,4}

B = {1,3,5,7}

Now

A ∩ B

= { x : x ∈ A ∧ x ∈ B }

= { 1 , 3 }

FINAL ANSWER

A ∩ B = { 1 , 3 }

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