Answer
a. "The set of all x in the universal set U such that x is in set A and x is in set B."
Shorthand notation: A ∩ B
b. "The set of all x in the universal set U such that x is in set A or x is in set B."
Shorthand notation: A ∪ B
c. "The set of all x in the universal set U such that x is in set A and x is not in set B."
Shorthand notation: A \ B
d. "The set of all x in the universal set U such that x is not in set A."
Shorthand notation: A
Work Step by Step
a. The set A ∩ B is the intersection of sets A and B. It contains all elements that are in both sets A and B. It is read as "the set of all x in the universal set U such that x is in set A and x is in set B." This means that if an element is a member of set A and also a member of set B, it will be included in the resulting set A ∩ B.
b. The set A ∪ B is the union of sets A and B. It contains all elements that are in either set A or set B, or in both sets. It is read as "the set of all x in the universal set U such that x is in set A or x is in set B." This means that if an element is a member of set A or a member of set B or both, it will be included in the resulting set A ∪ B.
c. The set A \ B is the relative complement of set B in set A. It contains all elements that are in set A but not in set B. It is read as "the set of all x in the universal set U such that x is in set A and x is not in set B." This means that if an element is a member of set A and is not a member of set B, it will be included in the resulting set A \ B.
d. The set A' is the complement of set A. It contains all elements that are not in set A. It is read as "the set of all x in the universal set U such that x is not in set A." This means that if an element is not a member of set A, it will be included in the resulting set A'.
