Question

Match the terms to their definition.

Part A
1. intersection of sets A and B is defined as any elements that are in either set A or set B
2. union of sets A and B is defined as any elements that are in both set A and set B
3. a statement formed by two or more inequalities
4. a member of a set
5. a collection or group of objects indicated by braces, { }
Part B
a. compound inequality
b. element
c. set
d. union
e. intersection

Answer 1

The correct matches are the intersection for common elements in both sets, union for all elements in either set, compound inequality for multiple inequalities, element for a set member, and set for a grouped collection of objects.

Step-by-step explanation:

To match the terms with their definitions, we need to understand the concepts represented by each term. Here is the correct matching:

1. Intersection of sets A and B (e. intersection) is defined as any elements that are in both set A and set B.
2. Union of sets A and B (d. union) is defined as any elements that are in either set A or set B.
3. A compound inequality (a. compound inequality) is a statement formed by two or more inequalities.
4. A member of a set (b. element) is a specific entity within that set.
5. A collection or group of objects indicated by braces, { } (c. set).

These definitions are essential to understanding basic concepts in set theory, a foundation for probability and other areas of mathematics. Recognizing these definitions helps in identifying the relationships between sets and the outcomes of events, especially when working with Venn diagrams and calculating probabilities.

Answer 2

a) 3

b) 4

c) 5

d) 1

e) 2

Step-by-step explanation:

Remember the key concepts for each part:

a) Compound inequalities are statements like a<x<b, which are equivalent to a<x and x<b (in this case, two inequalities). They can be formed by more inequalities, for example, 1<2<3<...<20 is a compound inequality formed of 19 inequalities (1<2, 2<3,.., 19<20).

b) Elements are related to sets by the membership relation, denoted by "∈". If A is a set, the statement "x∈A" means "x is a member of A" or "x is an element of A."

c) Sets are described as a collection of objects. These objects are said to belong to the set, that is, they are the elements of the set as in b).

d) If A and B are sets, the union of A and B, denoted by A∪B is the set whose elements are elements of A or elements of B. More formally, A∪B={x:x∈A is true or x∈B is true}. The word "or" used here is not exclusive: if x∈A and x∈B then x∈A∪B.

e) If A and B are sets, the intersection of A and B, denoted by A∩B is the set whose elements belong to A and belong to B. More formally, A∩B={x:x∈A is true and x∈B is true}.