Proving (A-B) U C ≤ (A U B U C) - (A n B)

[taylor81792]

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)

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. 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.

 

[Mark44]

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)

This is a statement about sets, so the relationship is $\subseteq$, not ≤.

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.

Try to be more careful with the names of the sets, which are A, B, and C, not a, b, and c.

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.

 

[mtayab1994]

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 :)

 

[taylor81792]

My professor said we can also try to prove or find a counterexample to this statement. Let A, B and C be sets. Then (A-B) U C = (A U B U C) - (A n B). I'm not really sure what she means by counterexample.

 

[HallsofIvy]

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 :)

Not only does that not help, it makes no sense. The left side is a set, the right side is a number.

Even if you meant |AUBUC| that is irrelevant to the problem. Showing that two sets have the same size does not prove they are the same set.