Question

EXERCISE 1.6
If X and Y are two sets such that n (X) = 17, n (Y) = 23 and n (XUY)= 38,
find n x intersection y by venn diagram​

Answer 1

$\large\bf\underline{Given:-}$

• X and Y are two sets
• n(X) = 17
• n(Y) = 23
• n(XUY)= 38

$\large\bf\underline {To \: find:-}$

• We need to find n(X∩Y)

$\huge\bf\underline{Solution:-}$

#Venn Diagram is in the attachment.

• n(X) = 17
• n(Y) = 23
• n(XUY) = 38
• n(X∩Y) (shaded part )= ?

we know that,

$\mid \boxed{ \tt \:n (X \: \cup \: Y) + n(X \: \cap \: Y) = n(X) + n(Y)} \mid$

BY using Formula :-

$\tt \:n (X \: \cup \: Y) + n(X \: \cap \: Y) = n(X) + n(Y) \\ \\ \tt \: n(X \: \cap \: Y) = n(X) + n(Y) - \:n (X \: \cup \: Y) \\ \\ \tt \: n(X \: \cap \: Y) = 17 + 23 - 38 \\ \\ \tt \: n(X \: \cap \: Y) = 40 - 38 \\ \\ \tt \: n(X \: \cap \: Y) = 2$

Hence,

▶️Value of n(X∩Y) = 2

$\rule{200}3$

Answer 2

GIVEN :-

• X and Y are two sets.

• n(X) = 17

• n(Y) = 23

• n(XUY) = 38

TO FIND :-

• n(X∩Y) = ?

SOLUTION :-

• Venn diagram in is the attachment,

• We know that,

=> n(XUY) + n(X∩Y) = n(X) + n(Y)

[ Put the values ]

=> 38 + n(X∩Y) = 17 + 23

=> 38 + n(X∩Y) = 40

=> n(X∩Y) = 40 - 38

=> n(X∩Y) = 2

Therefore,the value of n(X∩Y) is 2.