Functions Question 362
Question: Let R={$x|x\in N,x $ is a multiple of 3 and $ x\le 100$} S={$x|x\in N,x $ is a multiple of 5 and $ x\le 100$} What is the number of elements in $ (R\times S)\cap (S\times R) $
Options:
A) 36
B) 33
C) 20
D) 6
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let R = {$x:x\in N,x $ is a multiple of 3 and $ x\le 100$} and S = {$x:x\in N,x $ is a multiple of 5 and $ x\le 100$}
$ \therefore R={3,6,9,12,15…99} $ And $ S={5,10,15,…,95,100} $ Now, $ (R\times S)\cap (S\times R)=(R\cap S)\times (S\cap R) $ $ =(15,30,45,60,75,90)\times (15,30,45,60,75,90) $
$ \therefore $ Number of elements in $ (R\times S)\cap (S\times R) $ $ =6\times 6=36 $
BETA
