Question

Let A and B be two subsets of U such that
n(A) = 5, n(B) = n(A U B) = 7 and n(A')
= 12. Draw a Venn diagram to represent the
given sets. Also find:
a) n(A B)
b) n(B)
C) n(A U B)
d) n(A - B)
e) n(B - A)
f) n(U)

Answer 1

Let the number be xy , that is 10x+y .

Given, Sum of digits = x + y.

Question : The sum of digits of a number is subtracted from a number, the resulting number is always divisible by.

Number - Sum of digits

= ( 10 x + y) - ( x + y)

= 10x + y - x - y

= 10x - x + \cancel{ y }- \cancel{y}=10x−x+

y

−

y

= 9x .

So , 9x has factors 9 & x. Therefore, 9x is always divisible by 9 .

The sum of the digits of a number is subtracted from a number , the resulting number is always divisible by 9 .