在上文 LSAT逻辑推理题目的图形解法 2, 英语中的反向逻辑 中,我们熟悉了:
从形式逻辑的语言说。我们有:
if A, then B, => if no B, then no A.
但不能从 if A, then B, 推出 =》 if B , then A,
看下面这个问题 :
At Amen town hall, a total of seven workers are employed. These workers follow a daily schedule that is constrained by the following conditions:
If Anna is working, then Bill is also working.
If Bill is working, then Clarire is not working.
If Claire is working, then Dan and Emily are working
If Fanny is working, then Dan is woking.
If Gina is working, then Danis working and Anna is working.
所以用 O 表示working , X 表示 off working , 上面的图解表示应该是:
A O → B O,
B O → C X;
C O → D O and E O
F O → D O
G O→ D O and A O
Q1, Which of folloing is the complete list of people who could be working together?
A. A, B, and C
B G, D, A , and B
C E, A, C, and B
D G , D , A, and C
E F, D , G , and E
from A O → B O, and B O → C X; => A O → C X A, C 不能一起工作, 去掉 答案 A, C, D.
From G O→ D O and A O, and A O → B O, => 有 G 就 会有 B, 去掉 答案E,
所以正确答案是 B。
为什么这里我们还没有用到反向逻辑, if A, then B, => if no B, then no A. 这是题目决定的,在不用反向逻辑都可以推出答案的情况下。 就不用再多去考虑。
Q2. If G is working, then who must NOT be working?
A. A
B B
C C
D D
E E
Analysis: G O→ D O and A O => A O → B O, => B O → C X;
所以正确答案是 C。 只要前面分析正确, 后面都很容易 ,
Q3, If D is not working, then which of folloing is the complete list of people who CANNOT be working ?
A, C and E
B, B, A, and G
C. G, A, and B
D, G, E, and C
E, F, C, and G
Analysis: F O → D O => D X → F X.
C O → D O and E O => D X → C X.
G O→ D O and A O => D X → GX.
所以 答案 是 E: F, C, and G who CANNOT be working 。
注意,由于问题关系,我们 又开始要用到反向逻辑, 比如
从 C O → D O and E O ,我们得到 D X → C X. ,但是我们不可以得到 D X → E X 的推论, 应为如果 C 工作的话,D 一定也在工作, 所以, D不工作,C也一定不工作, 但是, D不工作 跟 E没有关系。
Q4. If E is not working, then who of folloing must NOT be working?
A. C
B. D
C. B
D. G
E. A
Analysis: C O → D O and E O => E X → C X
answer is A. C.
