Question

Which of the following sets can be the universal set of $A=\{10,20,30,...\}$

• A. Set of all Multiples of $5$
• B. Set of all even natural numbers
• C. Set of all odd natural numbers
• D. Set of all multiples of $20$

Answer 1

Answer: (A), (B)

Set of all even natural numbers

Given set $A=\{10,20,30,...\}$ which can be interpreted as a set of all multiples of $10.$
Now, any set can be an universal set for $A,$ if that set is a superset of $A.$
Here, Set of all multiples of 5 can be written as $\{5,10,15,20,25,...\}$ which is clearly a superset of $A=\{10,20,30,...\}$

Set of all even natural numbers can be written as $\{2,4,6,8,10,12,14,...\}$ which is also a superset of $A=\{10,20,30,...\}$

Set of all odd natural numbers can be written as $\{3,5,7,9,11,13,...\}$ which is clearly not a superset of $A.$

Set of all multiples of 20 can be written as $\{20,40,60,80,100,...\}$ which is clearly not a superset of $A.$

Thus, from the given options, Set of all multiples of $5$ and set of all even natural numbers can be the universal set of the set.