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
)
.]


Choose the correct option(s) from below.

625 is in
E
.

G
is an empty set.

200 is in
G

2500 is in
F

2500 is in
G

25 is in
F

A
and
F
are empty.

Answer 1

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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