Question

If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?
NCERT Solutions for Class 11th Mathematics Chapter 1 Exercise 1.6 5

Answer 1

Answer :
     n(X) = 40
     n(Y) = ?    
X ∪ Y = 60
X ∩ Y = 10 

we know that ,
 
X ∪ Y = n(X) + n(Y) -
X ∩ Y

substitute the values , we get
60 = 40 + n(Y) - 10
 60 = 50 + n(Y)
or 60 - 50 = n(Y)
or 10 = n(Y)
or n(Y) = 10 .

hence Set Y has 10 elements .

Thank You!!

Answer 2

$\huge\pink{\mid{\underline {\overline{\tt ❥︎A᭄ɴsᴡᴇʀ࿐✪}}\mid}}$

It is given that,

n(X)=40

n(X∪Y)=60

n(X∩Y)=10

We know that

n(X∪Y)=n(X)+n(Y)–n(X∩Y)

∴60=40+n(Y)–10

∴n(Y)=60–(40–10)=30

Thus, the set Y has 30 elements.

$\boxed{\fcolorbox{Blue}{Red}{\color{yellow}{hope\:it\:helps\: you}}}$