数学讨论

sabrinallj · 发表于 2013-9-17 16:36:28

各位高人，恕我数学白痴，正在研究CXD的那本数学，有道DS题目不会做。
有哪位可以教教我？请详解。跪谢！
If P is a set of Intergers and 3 is in P, is every positive multiple of 3 in P?
1) If X is in P, then X+3 is in P
2) If X is in P, then X-3 is in P
我想选D, 可是答案是A

turndd · 发表于 2013-9-17 16:58:15

consider condition 1) first. we got two conditions altogether
3 is in p
x is in p, then x+3 is in p
hence 3 is in p, 3 + 3 is in p; hence 6 is in p, 6+3 is in p, ..., till infinity.
all positive multiple of 3, including 3 6 9 12 15 .... 3n, are in p

now consider condition 2), under the same anology,
we will only have 3 0 -3 -6, ... , till minus infinity.
clearly all multiply of 3 are not contained in set P.

sabrinallj · 发表于 2013-9-17 17:45:55

turndd 发表于 2013-9-17 16:58
consider condition 1) first. we got two conditions altogether
3 is in p
x is in p, then x+3 is in p

Great thanks for your feedback!
However, in Condition 2, what if X=9, then X-3=6 is also in P; if X=12, then X-3=9 is also in P, till infinity...... in this way, every multiple of 3 are also in the set P..... Does my thoughts make sense? Must have some flaws somewhere....but I just don't know where it is.......sorry.
Do you know where my mistake is?? Thanks!!!

turndd · 发表于 2013-9-17 18:34:58

sabrinallj 发表于 2013-9-17 17:45
Great thanks for your feedback!
However, in Condition 2, what if X=9, then X-3=6 is also in P; if ...

Nope, the question never mentions about 9, the number you start count down with, is in set P.
And even if the question mentioned a very large multiply of 3, marked as "a" for convenience, is in set P, still it would be not enough to say that a+3, another multiply of 3, sits in set P.

Alternatively, you may have a problem distinguish between what is a condition and what is a conclusion.
in your analogy, you misuse x-3 as a condition and deduce the result involving x. Here you commit a logic error.

sabrinallj · 发表于 2013-9-17 20:42:22

turndd 发表于 2013-9-17 18:34
Nope, the question never mentions about 9, the number you start count down with, is in set P.
And ...

You are so great! Now I'm clear!!! Thanks again for help!!!

数学讨论

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