Ilmu Khan #9 - Let's try using the definition of \\(\vee\\). By definition, \\(A \vee B\\) is the least (=smallest) element \\(X\\) such that \\(A \le X\\) and \\(B \le X\\). So question 6) is asking us this:

> Supopose \\(A \le C\\) and \\(B \le C\\) and \\(X\\) is the smallest element such that \\(A \le X\\) and \\(B \le X\\). Does this imply \\(X \le C\\)?

> Supopose \\(A \le C\\) and \\(B \le C\\) and \\(X\\) is the smallest element such that \\(A \le X\\) and \\(B \le X\\). Does this imply \\(X \le C\\)?