The problem involves proving the set relationship (A - B) U C ⊆ (A U B U C) - (A ∩ B), which pertains to set theory and the properties of unions and intersections of sets.
The discussion is ongoing, with participants sharing their attempts and questioning the clarity of the problem statement. Some guidance has been offered regarding the use of set notation, but no consensus has been reached on the approach to take.
There is a noted confusion regarding the use of symbols and terminology, particularly the distinction between set relationships and numerical comparisons. Additionally, the professor's suggestion to consider counterexamples introduces an element of exploration into the discussion.
This is a statement about sets, so the relationship is \subseteq, not ≤.taylor81792 said:Homework Statement
The problem I have been given is to prove (A - B) U C is than less or equal to (A U B U C) - (A n B)
Try to be more careful with the names of the sets, which are A, B, and C, not a, b, and c.taylor81792 said:The Attempt at a Solution
I've tried starting off with just (A-B) U C. Then I would say how x ε c or x ε (A - B). Also if x ε a, then x ε c and x is not in b.
taylor81792 said:If x ε c, since c is a subset of (A U B U C) , x ε (A U B U C). I don't know if this is right or where to go from here.
Not only does that not help, it makes no sense. The left side is a set, the right side is a number.mtayab1994 said:i'd say that u can use:
AUBUC= lAl + lBl + lCl - lBnCl - lAnBl - lAnCl+lAnBnCl
but I'm not 100% positive just trying to give some help :)