Question

Let X be the set of natural numbers divisible by 100, Y be the set of natural numbers divisible by 25, Z be the set of natural numbers which are perfect squares. Now consider the following Venn diagram. [Note: A , B , C , D , E , F , G are the region marked in the following Venn diagram (A region in the Venn-diagram can be an empty). For example, A = X ∖ ( Y ∪ Z ) , B = Y ∖ ( X ∪ Z ) , a n d C = Z ∖ ( X ∪ Y ) .]


1: 625 is in E



2: G is an empty set.


3: 200 is in G


4: 2500 is in F


5: 2500 is in G


6: 25 is in F


7: A and F are empty.

Answer 1

Answer:

A is an Empty set as there are no natural nos divisible by 100 which is not present either in Y or Z

B has elements such as 50,75,125,150,175,250,275......which are not present in either X or Z

C has elements such as 1,4,9,16,36,49,64,81,121... which are not present in X or Y

A B & C has no elements in common hence

D E F & G is also empty option 2 & 7 is correct.

Which means only

Answer 2

Given   X be the set of natural numbers divisible by 100, Y be the set of natural numbers divisible by 25, Z be the set of natural numbers which are perfect squares

To Find : Which are correct

1: 625 is in E

2: G is an empty set.

3: 200 is in G

4: 2500 is in F

5: 2500 is in G

6: 25 is in F

7: A and F are empty.

Solution:

X = { 100 , 200 , 300 , .........................., }

Y = { 25 , 50 , 75 , 100 , .......................}

Z = {  1 , 4 , 9 , .......................................}

625 is in E - TRUE   as  625 = 25² = 25 * 25   Perfect square & divisible by 25  but not divisible by 100  

G is an empty set  - FALSE   as  100  is perfect square , divisible by 25 & 100

also 400 , 900 and so on

200 is in G    - FALSE  as 200 is not a perfect square

2500 is in F     FALSE  as 2500 is also divisible by 25 Hence in G

25 is in F  FALSE as not divisible by 100  but divisible by 25

A and F are empty.  - TRUE

A  = Empty set  as      X is also divisible by 25    

F  = Empty set  as      It is also divisible by 25    

 

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