The discussion centers on proving the set relationship (A - B) U C ⊆ (A U B U C) - (A ∩ B). Participants emphasize the importance of correctly identifying set notation and relationships. A suggestion is made to utilize the formula |A U B U C| = |A| + |B| + |C| - |B ∩ C| - |A ∩ B| - |A ∩ C| + |A ∩ B ∩ C|, although its relevance to the proof is questioned. The need for clarity in distinguishing between set equality and cardinality is highlighted, as proving set equality requires demonstrating that both sets contain the same elements.
PREREQUISITESStudents of mathematics, particularly those studying set theory, logic, and proof techniques, as well as educators seeking to clarify set relationships in their teaching materials.
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 :)