mharten1 said:Homework Statement
Construct the negation of each statement below without using the fol-
lowing symbols: ∩, ∪, ⊆, ⊇, ⊂, ⊃, \, △, and =.
x ∈ A U B
Homework Equations
The Attempt at a Solution
I don't even know where to start. I'm completely lost. =\
Zondrina said:Well, my guess is you want to negate the statement : x ∈ AUB.
This statement means that either x is in A or x is in B. How do you NEGATE this proposition?
mharten1 said:X is not in A or B? How do I symbolically write that? Because I can't use the union symbol. I initially thought that but it seemed too simple.
Zondrina said:The negation operator is written as : [itex]\neg[/itex]
mharten1 said:Ok, that makes sense. But I can't use the union symbol, and that's where I'm really confused.
Zondrina said:Well you're not being very clear about what statements you're trying to negate. Are they phrases that you haven't posted or is it actually the statement : x∈AUB. If you're trying to negate x∈AUB, then you can take for granted that the question is ASKING you to negate that statement, you're simply just not allowed to use the union symbol in doing it.
mharten1 said:It's actually the statement x ∈ AUB.
Zondrina said:Like I've already stated before then, if x ∈ AUB then either x is in A or x is in B. How would you negate this proposition, aka write the opposite of what this means.
mharten1 said:I would do ~(A v B), which simplifies to ~A ^ ~B. But as far as I know A and B are sets so I can't use those symbols.
"Negation AUB" is a mathematical term that refers to the negation of the union of two sets, denoted as ¬(A∪B). In simpler terms, it means the set of elements that are not in either set A or set B.
The difference between "Negation AUB" and "A∩B" is that "Negation AUB" includes elements that are not in either set A or B, while "A∩B" only includes elements that are common to both set A and set B.
In a Venn diagram, "Negation AUB" can be represented as the area outside of the overlapping region between sets A and B. This area includes all elements that are not in either set A or set B.
The relationship between "Negation AUB" and the complement of "A∪B" is that they are equivalent. Both represent the set of elements that are not in either set A or set B.
"Negation AUB" can be used in real-life scenarios to represent situations where an outcome is not the result of either of two events. For example, if event A is getting a job offer and event B is getting a promotion, "Negation AUB" would represent not getting a job offer or a promotion, or getting neither a job offer nor a promotion.