Sets-Relations-And-Functions Question 145
Question: Let $A=\{x \mid x \leq 9, x \in N\}$. Let $B=\{a, b, c\}$ be the subset of A where $(a+b+c)$ is a multiple of 3 . What is the largest possible number of subsets like B?
Options:
A) 12
B) 21
C) 27
D) 30
Correct Answer: D Total possible multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27 But 3 and 27 are not possible because 3 and 27 cannot be express as such that $ a+b+c $ multiple of 3 $ 6\to 1+2+3 $ $ 9\to 2+3+4,5+3+1,6+2+1 $ $ 12\to 9+2+1,8+3+1,7+1+4,7+2+3 $ $ 6+4+2,6+5+1,5+4+3 $ $ 15\to 9+4+2,9+5+1,8+6+1,8+5+2, $ $ 8+4+3,7+6+2,7+5+3,6+5+4 $ $ 18\to 9+8+1,9+7+2,9+6+3, $ $ 9+5+4,8+7+3,8+6+4,7+6+5 $ $ 21\to 9+8+4,9+7+5,8+7+6 $ $ 24\to 9+8+7 $
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Answer:
Solution:
Hence, total largest possible subsets are 30.
BETA
