Let A and B be sets. Below are listed several statements involving set notation. For each case, write a statement in words that says what is written in symbols.
a. A U B
b. A ∩ B
c. A ⊆ B
d. a ∈ A
e. A ∩ B = Ø
a. The symbol A U B represents the union of sets A and B. In other words, it is the set that contains all the elements that are in either set A or set B, or both.
b. The symbol A ∩ B represents the intersection of sets A and B. This is the set that contains all the elements that are common to both sets A and B.
c. The symbol A ⊆ B represents the subset relationship between sets A and B. This statement means that every element in set A is also an element of set B, or in simpler terms, set A is a subset of set B.
d. The statement a ∈ A means that the element 'a' is an element (or member) of set A. In other words, a is one of the elements contained in set A.
e. The equation A ∩ B = Ø represents the empty or null set. This means that sets A and B have no elements in common, resulting in an empty set as their intersection.