Question

Let $A = \{2, 4, 6, 9\}$ and $B = \{4, 6, 18, 27, 81\}$. If $C = \{(x, y) \mid x \in A, y \in B$ such that $x$ is a factor of $y$ and $x<y\}$, then $n(C)$ is:

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

Manually verify pairs $(x, y)$ that satisfy both conditions: $x$ divides $y$ and $x<y$.

Answer 1

The Correct Option is A

Check all $(x,y)$ pairs such that $x<y$ and $x$ divides $y$: - $x = 2$: $y = 18$ - $x = 4$: $y = 4$ \((not <)\), $y = 18$ - $x = 6$: $y = 18$ - $x = 9$: $y = 27$ Valid pairs: (2,18), (4,18), (6,18), (9,27), (9,81) → Total = 5