Sets 1

Determine which of the following sets is finite or infinite. Write the cardinality of each of the finite sets.

𝐴=𝑠𝑒𝑡 𝑜𝑓 𝑚𝑜𝑛𝑡ℎ𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟

(a)  

Answer explanation

Finite

Determine which of the following sets is finite or infinite. Write the cardinality of each of the finite sets.

𝐵 = {2,4,6,8,…}

(a)  

𝐶 = {𝑥|𝑥 𝑖𝑠 𝑎 𝑤ℎ𝑜𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑛𝑑𝑥 ≥1000}

Is this set finite or infinite

(a)  

𝑆 ={𝑠|𝑠 ∈ℝ, 𝑠2−𝑠−2=0}, Is this ​

• Finite
• infinite
• Undecided

List the elements of the set

𝑇 = 𝑠𝑒𝑡 𝑜𝑓 𝑙𝑒𝑡𝑡𝑒𝑟𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑜𝑟𝑑 "𝑓𝑜𝑙𝑙𝑜𝑤“

(a)  

List the elements of the following interval in set notation,

N = [-5,4)

(a)  

The following set builder notation in plain English is:

𝑀 = {𝑚|𝑚∈ℕ,3 ≤ 𝑥 < 7}

• M is the set of m such that m is an even integer and 𝑥>3.

• M is the set of m such that m is greater or equal to 3 and less than 7.

• M is the set of m such that m is an integer.

• M is the set of m such that m is between 3 and 7.

Let 𝐴 = 𝑥|2𝑥 = 6 and let 𝑏 = 3. Does 𝑏 =𝐴?

• yes
• no

• can't tell

d ∈ 𝐴

• d is a member of E

• d is not a member of E

• d is a subset of E

• d is not a subset of E

Represent the following sets using the interval notation.

a) 𝐼1 = {𝑥|𝑥∈ℝ,1≤𝑥≤6}

b) 𝐼2 = {𝑥|𝑥∈ℝ,−7<𝑥≤4}

c) 𝐼3 = {𝑥|𝑥∈ℝ,0≤𝑥<𝜋}

d) 𝐼4 = {𝑥|𝑥∈ℝ,𝑥≤7}