Let A=(-2,INF] and B=(2,INF). FIND:
a.)AUB
b.)A (UPSIDE DOWN "U")B
c.)A\B
d)B\A
*I was thinking a was (-2,inf), b was (-1,2), c was (-1,1) and d was (2,inf) but i don't think that is right since i don't have a U in the answers.
To find the answers to these set operations, let's break down what each operation means:
a.) A U B represents the union of sets A and B. The union of sets is the combination of all elements from both sets, without any repetition.
b.) A ∩ B represents the intersection of sets A and B. The intersection of sets is the collection of elements that are common to both sets.
c.) A \ B represents the set difference or relative complement of B in A. It is the set of elements that are present in A but not in B.
d.) B \ A represents the set difference or relative complement of A in B. It is the set of elements that are present in B but not in A.
Let's calculate each of these:
a.) A U B:
To find the union of these sets, we need to combine all the elements from both sets, without repetition.
For set A=(-2,inf], it includes all real numbers greater than or equal to -2.
For set B=(2,inf), it includes all real numbers greater than 2.
Combining these two sets, we get (-2,inf] U (2,inf), which represents all real numbers greater than -2 or greater than 2.
b.) A ∩ B:
To find the intersection of these sets, we need to identify the elements that are common to both sets.
Set A=(-2,inf] includes all real numbers greater than or equal to -2.
Set B=(2,inf) includes all real numbers greater than 2.
Since there are no elements that satisfy both conditions, the intersection A ∩ B is an empty set.
c.) A \ B:
To find the set difference of B in A (A \ B), we need to identify the elements that are in A but not in B.
Set A=(-2, inf] includes all real numbers greater than or equal to -2.
Set B=(2,inf) includes all real numbers greater than 2.
Therefore, A \ B represents all real numbers greater than or equal to -2, but not greater than 2. In interval notation, this can be expressed as (-2,2].
d.) B \ A:
To find the set difference of A in B (B \ A), we need to identify the elements that are in B but not in A.
Set A=(-2, inf] includes all real numbers greater than or equal to -2.
Set B=(2,inf) includes all real numbers greater than 2.
Since set A does not include any numbers greater than 2, B \ A is equivalent to set B. So B \ A represents all real numbers greater than 2, in interval notation (2,inf).
Therefore, the correct answers are:
a.) A U B = (-2,inf] U (2,inf)
b.) A ∩ B = Empty set
c.) A \ B = (-2,2]
d.) B \ A = (2,inf)