Exploring Sets and Their Operations

What is the set notation for the set of all even numbers?

• { n ∈ Z | n = 2k + 1, k ∈ Z }

• { n ∈ Z | n = 2k, k ∈ Z }

• { n ∈ Z | n = k^2, k ∈ Z }

• { n ∈ Z | n = 3k, k ∈ Z }

Classify the following set: {1, 2, 3, 4, 5}. Is it finite or infinite?

• finite

• infinite

• undefined

• countably infinite

Draw a Venn diagram to represent the sets A = {1, 2, 3} and B = {3, 4, 5}.

• A Venn diagram with two circles: left circle (A) has 3; right circle (B) has 4, 5; overlap has 1, 2.

• A Venn diagram with one circle containing 1, 2, 3; no overlap.

• A Venn diagram with two circles: left circle (A) has 1; right circle (B) has 3, 4, 5; overlap is empty.

• A Venn diagram with two circles: left circle (A) has 1, 2; right circle (B) has 4, 5; overlap has 3.

What is the union of the sets A = {a, b, c} and B = {b, c, d}?

• {a, c, d}

• {a, b, c, d}

• {a, b}

• {b, c, d, e}

Identify the complement of the set A = {1, 2, 3} in the universal set U = {1, 2, 3, 4, 5}.

• {3, 4}

• {1, 2}

• {2, 3}

• {4, 5}

Is the set {x | x is a prime number less than 10} a finite or infinite set?

• finite

• countably infinite

• empty

• infinite

Construct a Venn diagram for the sets X = {1, 2} and Y = {2, 3, 4}.

• Venn diagram with X: {2}, Y: {3, 4}, intersection: {}, unique to X: {}, unique to Y: {3, 4}

• Venn diagram with X: {1, 2}, Y: {2, 3, 4}, intersection: {2}, unique to X: {1}, unique to Y: {3, 4}

• Venn diagram with X: {1, 2, 3}, Y: {2, 4}, intersection: {2}, unique to X: {1, 3}, unique to Y: {4}

• Venn diagram with X: {1}, Y: {2, 3, 4}, intersection: {}, unique to X: {1}, unique to Y: {2, 3, 4}

What is the intersection of the sets A = {2, 4, 6} and B = {1, 2, 3, 4}?

• {2, 3, 4}

• {1, 3}

• {2, 4}

• {4, 6}

If A = {x | x is a natural number} and B = {x | x is an even number}, what is A - B?

• {x | x is a natural number and x is odd}

• {x | x is a natural number and x is negative}

• {x | x is a natural number and x is prime}

• {x | x is a natural number and x is even}

Classify the set {0, 1, 2, 3, 4, 5} as a subset of the set of integers. Is it a proper subset?

• It is an empty set and cannot be classified.

• Yes, it is a subset but not a proper subset.

• Yes, it is a proper subset of the set of integers.

• No, it is not a subset of the set of integers.