Help-How to Prove It, Sec.4.4, 18b

[IntroAnalysis]

Homework Statement

The real problem is my professor makes anyone who asks a question in class or office hours feel like a total idiot. I

Sec.4.4 Problem 18a) https://www.physicsforums.com/showthread.php?t=541479

Could someone comment on whether it would be okay to use part a) in part b)?

Homework Equations

Above we proved, for all x element of A, x is an upper bound of B1 iff x is an upper bound of B2.
Can we use this in part b)? Although b) is talking about a maximal element instead of an upper bound. I think the only difference is that maximal element is part of the subset.

The Attempt at a Solution

Contra positive. Assume B1 has a maximal element b1. This means that there does not exist an x є B1(b1Rx Λ b1 ≠ x). By part a), we know that b1 is also the maximal element of B2. Therefore, b1 є (B1 and B2). Therefore, B1 and B2 are not disjoint.

 

[mighty2000]

As a fellow scientist, I understand your frustration with your professor's behavior. It can be difficult to learn and ask questions in an environment where you feel belittled or inadequate. However, let's focus on the problem at hand.

In part a), you proved that for all x in A, x is an upper bound of B1 if and only if x is an upper bound of B2. This statement is true for all elements in A, not just maximal elements. Therefore, you cannot directly apply this statement to part b) which specifically deals with maximal elements.

In order to solve part b), you need to use the definition of a maximal element. A maximal element is an element that is greater than or equal to all other elements in the set. So, if you have a maximal element b1 in B1, you need to show that it is also a maximal element in B2. This can be done by assuming that there exists an element b2 in B2 that is greater than b1. This would contradict the fact that b1 is a maximal element in B1. Therefore, b1 must also be a maximal element in B2.

I hope this helps. Remember, it's always okay to ask for clarification or assistance, even if your professor makes you feel otherwise. Keep persevering!