Question

If P = { x | x is a multiple of 10 } and
Q = { x | the unit’s (ones place )digit of x is not zero} then P ∩ Q is equal to .

• A. P ∩ P
• B. P ∩ $\varphi$
• C. P

Answer 1

The correct option is B P ∩ $\varphi$

P = { x | x is a multiple of 10 }

P = { 10, 20, 30, 40, 50, … }

Q = { x | the unit’s (ones place )digit of x is not zero}

Q = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12,… } ---> all elements except 10, 20, 30,…

So, there is no common element between set A and B.

∴ P ∩ Q = $\varphi$ = P ∩ $\varphi$