Question

E={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} A={x:x is a multiple of 3} B={x:x is a factor of 24} C={x:x is an odd number} (i) Find (a) n(B),

Answer 1

B={1,2,3,4,6,8,12,24}

n(B)=8

Answer 2

`\boxed{ \huge{ \bold{ \boxed{ \sf{3 \:  ,  \: 6 \:  ,  \: 12}}}}}`

Explanation:

Given,

E = { 1 , 2 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 }

Here, E is the universal set.

A = { x : x is a multiple of 3 }

Here, we have to list the multiples of 3 less than 16

A = { 3 , 6 , 9 , 12 , 15 }

B = { x : x is a factor of 24 }

Here, we have to list the factors of 24 less than 16 }

Factor of 24 means the numbers that can divide 24 easily.

Factor of 24 includes :

B = { 1 , 2 , 3 , 4 , 6 , 8 , 12 }

C = { x : x is an odd number }

Here, we have to list the odd numbers which are less than 16

C = { 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 }

Finding A ∩ B

Here, We have to find the common elements that are present in both A and B

{ 3 , 6 , 9 , 12 , 15 } ∩ { 1 , 2 , 3 , 4 , 6 , 8 , 12 }

= { 3 , 6 , 12 }

Hope I helped!

Best regards!!