What is a finite set?

A finite set is a set that has a specific, countable number of elements. For example, the set of all even numbers less than 10 is finite: {2, 4, 6, 8}.

What is the difference between a subset and a proper subset?

A subset A of a set B includes all elements of A that are also in B. A proper subset A of B means A is a subset of B but not equal to B, meaning A contains fewer elements than B.

What is the formula for the union of two sets?

The formula for the union of two sets A and B is n(A ∪ B) = n(A) + n(B) - n(A ∩ B). For example, if n(A) = 3 and n(B) = 4 with n(A ∩ B) = 1, then n(A ∪ B) = 3 + 4 - 1 = 6.

What is the formula for the complement of a set?

The complement of set A, denoted as Ac, is defined as Ac = U - A, where U is the universal set. For example, if U = {1, 2, 3, 4, 5} and A = {2, 4}, then Ac = {1, 3, 5}.

What is a quick way to determine if a set is empty?

To determine if a set is empty, check if there are no elements listed in roster form or no defining property in set-builder form. For example, Ø denotes an empty set.

How can you quickly find the number of subsets of a set?

The number of subsets of a set with n elements is given by 2^n. For example, if a set has 3 elements, the number of subsets is 2^3 = 8.

If U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?

A' is the complement of A with respect to U. Therefore, A' = U - A = {3, 4, 5}.

If A = {x | x is an odd integer less than 10} and B = {x | x is a prime number less than 10}, what is A ∩ B?

A ∩ B = {3, 5, 7} because these are the elements that are both in A and B.

What is the power set of A = {a, b}?

The power set of A, denoted P(A), is the set of all subsets of A. Thus, P(A) = {Ø, {a}, {b}, {a, b}}.

Given A = {1, 2} and B = {2, 3}, what is A ∪ B?

A ∪ B = {1, 2, 3}. It includes all elements from both sets without duplication.

What is an equivalent set?

Two sets are equivalent if they have the same number of elements, regardless of what the elements are. For example, A = {1, 2} and B = {x, y} are equivalent sets.

What is the formula for the intersection of two disjoint sets?

If A and B are disjoint sets, then n(A ∩ B) = 0. For example, if A = {1, 2} and B = {3, 4}, then n(A ∩ B) = 0.

How can knowing the universal set help in solving set problems?

Knowing the universal set allows you to easily find complements and determine relationships between sets. It provides a reference for which elements are included or excluded.

If A = {x | x is a vowel} and B = {x | x is a consonant}, what is A ∩ B?

A ∩ B = Ø since there are no elements that are both vowels and consonants.

What is the definition of a subset?

A set A is a subset of a set B, denoted as A ⊆ B, if every element of A is also an element of B. For example, if A = {1, 2} and B = {1, 2, 3}, then A is a subset of B.