If Norton is scheduled for the fifth performance, which one of the following could be true?
NicoCapriJune 20, 2014
Contrapositive confusion
I am a bit confused on certain contrapositive conditions. For example, you mention in game 4 from the lecture that the contrapositive of rule 4 would mean that if Lopez does not go on day 5 then Knight cannot go on day 4. However, I do not see how these conditions are mutually exclusive. Why can't Lopez go on day 5 without Knight on day 4? In some games this would not be the case (Lopez could go on 5 without Knight on 4, but if Knight is on 4 then Lopez would have to be on 5).
An example of a similar situation where they are not mutually exclusive conditions is from this homework game (December 1997):
The rule for this game states that "Lalitha performs 3rd only if Norton performs 5th". However, in question 8 Norton is 5th and Lalitha is not 3rd.
How do you decipher between these two types of conditional situations?
Replies
Create a free account to read and
take part in forum discussions.
The necessary conditions of either one of those rules are not mutually exclusive. Let's take the following example: If A, then not B.
A ==> not B B ==> not A
The necessary conditions "not B" and "not A" are not mutually exclusive. They can both occur at the same time. Since they are necessary conditions, they do not invoke anything else.
Therefore, in the lecture, Lopez can go on day 5 even if Knight does not go on day 4. That is a completely acceptable scenario. Similarly, in this game, Norton can perform fifth even if Lalitha does not perform third.
They are not "two types of conditional situations." In all Sufficient & Necessary statements the necessary conditions of the statement and its contrapositive can be a valid scenario.
Hope that was helpful! Let us know if you have any other questions.
MarieNovember 18, 2018
I have the same question.
I dont' understand it either, sorry, for the same reason as nicolette
Jacob-RNovember 20, 2018
Hi @Marie
Perhaps it would be helpful to illustrate necessary conditions (and their contrapositive) with a real example.
Imagine you are eating breakfast. IF you have cereal, you eat it with milk. [Contrapositive: If you are not having milk, you are not having cereal.]
And another condition: IF you have toast, you eat it with jam. [If you don’t have jam, you aren’t having toast.]
None of the conditions I just laid out are mutually exclusive. You could have cereal (with milk) and also have toast (with jam), or you could not have jam and not have milk, and we would know you are not having cereal or toast either. Or you could have one pair and not the other.
The main point here is always just to carefully think through — am I violating any rule? If not, then you are likely fine!
