Part (a)
Answer: Ø
This is the empty set
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Explanation:
It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.
This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.
We can write Ø as { } which is a set of curly braces with nothing inside it.
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Part (b)
Answer: {1,2,3,4,5,6}
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Explanation:
When you union the universal set with any other set, you'll get the universal set.
The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.
Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.
It's like saying
- A = set of stuff inside a persons house
- [tex]\overline{A}[/tex] = set of stuff outside a persons house (ie stuff that is not in set A)
- U = set of every item
we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.
