Question

Let the Universal set be U= {0,1,2,……9} and A= {1,2,4,6,8} , B ={2,3,5,8} and
C={2,5,6,7}. Draw the Venn diagram to represent these sets, also find:

(i) (A ∩B)’ (ii) (B-A)​

Answer 1

i) (A ∩ B)’ = U - (A ∩ B) = {0, 1, 3, 4, 5, 6, 7, 9}. With the help of venn diagram.

ii)  (B - A) = {3, 5}.

To draw the Venn diagram representing the given sets A, B, and C, we can start by plotting the elements of each set within the universal set U.

Universal set U: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Set A: {1, 2, 4, 6, 8}

Set B: {2, 3, 5, 8}

Set C: {2, 5, 6, 7}

Now, let's construct the Venn diagram:

A: {1, 2, 4, 6, 8}

__________________

| __________|

| | |

| B: {2, 3, 5, 8}|

| ___________ |

| | ||

| C: {2, 5, 6, 7} ||

| ___________ ||

| | ||

|______________|||

In the Venn diagram, the overlapping regions represent the intersections between the sets. For example, the region where A and B overlap represents the elements common to both A and B, which are {2, 8}.

Now, let's calculate the requested values:

(i) (A ∩ B)’ represents the complement of the intersection of sets A and B. In other words, it represents the elements that are in neither A nor B. To find this, we need to consider the elements in the universal set U that are not in the intersection of A and B.

Intersection of A and B: A ∩ B = {2, 8}Complement of A ∩ B: (A ∩ B)’ = U - (A ∩ B) = {0, 1, 3, 4, 5, 6, 7, 9}

(ii) (B - A) represents the elements that are in B but not in A. It represents the elements unique to B.

Elements in B: {2, 3, 5, 8}

Elements in A: {1, 2, 4, 6, 8}

To find (B - A), we need to remove the elements common to A and B from B.

(B - A) = {3, 5}

For more such questions on  venn diagram visit:

https://brainly.in/question/34415387

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