Question

Let $A = { (n, 2n) : n \in N}$ and B = {$(2n, 3n) : n \in N $}. What is A $\cap$ B equal to ?

• A. {$(n, 6n) : n \in N$}
• B. {$(2n, 6n) : n \in N$}
• C. {$(n, 3n) : n \in N$}
• D. $\phi$

Answer 1

Answer: (D)

$A = {(n, 2n) : n \in N}$ and B = {(2n, 3n)}: $n \in N$
Listing few members of each set
A = {(1, 2), (2, 4), (3, 6),....}
B = {(2, 3), (4, 6), (6, 9)......}
There is no member common to both these sets, hence.
$A \cap B = \phi$