Math 301 Exam 1 (Module 1) | 2025/2026
UPDATE | QUESTIONS AND ANSWERS | WITH
COMPLETE SOLUTION
(A and B are sets)
What is A ∪ B? - ANSWERS-The union of A and B. Set of elements that are in
A OR B (or both)
(A and B are sets)
What is A ∩ B? - ANSWERS-The intersection of A and B. A set of elements
that are in both A AND B. What does |A| mean? - ANSWERS-cardinality of A
combinatorial proof - ANSWERS-A proof that makes use of counting
principles
To prove an equation of the form LHS = RHS:
Pose a question of the form, "In how many ways . . . ?"
On the one hand, argue why LHS is a correct answer to the question.
On the other hand, argue why RHS is a correct answer.
Therefore LHS = RHS.
, When are A and B disjoint? - ANSWERS-when A ∩ B = Ø
Let A and B be finite sets. Then
|A| + |B| = ? - ANSWERS-| A U B | + | A ∩ B |
Addition principle - ANSWERS-Let A and B be finite sets.
If A and B are disjoint, then |A U B| = |A| + |B|
A - B is a set of elements that include?
ex) A = {1,2,3,4} B = {3,4,5,6}
A-B=?
how to write in symbols? - ANSWERS-the set of all elements of A that are
not in B
How can you write A ∪ B in symbols? - ANSWERS-{x: x ∈ A or x ∈ B}
How can you write A ∩ B in symbols? - ANSWERS-{x: x ∈ A and x ∈ B}
Suppose A = {1, 2, 3} and B = {3, 4, 5}, what is:
A∪B
and
UPDATE | QUESTIONS AND ANSWERS | WITH
COMPLETE SOLUTION
(A and B are sets)
What is A ∪ B? - ANSWERS-The union of A and B. Set of elements that are in
A OR B (or both)
(A and B are sets)
What is A ∩ B? - ANSWERS-The intersection of A and B. A set of elements
that are in both A AND B. What does |A| mean? - ANSWERS-cardinality of A
combinatorial proof - ANSWERS-A proof that makes use of counting
principles
To prove an equation of the form LHS = RHS:
Pose a question of the form, "In how many ways . . . ?"
On the one hand, argue why LHS is a correct answer to the question.
On the other hand, argue why RHS is a correct answer.
Therefore LHS = RHS.
, When are A and B disjoint? - ANSWERS-when A ∩ B = Ø
Let A and B be finite sets. Then
|A| + |B| = ? - ANSWERS-| A U B | + | A ∩ B |
Addition principle - ANSWERS-Let A and B be finite sets.
If A and B are disjoint, then |A U B| = |A| + |B|
A - B is a set of elements that include?
ex) A = {1,2,3,4} B = {3,4,5,6}
A-B=?
how to write in symbols? - ANSWERS-the set of all elements of A that are
not in B
How can you write A ∪ B in symbols? - ANSWERS-{x: x ∈ A or x ∈ B}
How can you write A ∩ B in symbols? - ANSWERS-{x: x ∈ A and x ∈ B}
Suppose A = {1, 2, 3} and B = {3, 4, 5}, what is:
A∪B
and
