Question

Create a set of numbers and call the set N. Describe a subset of N and explain why it is a subset of N.

Answer 1

if N is a set of numbers, then if you take numbers from N and put them in another set (let's call it M), by definition M is a subset of N, as all of it's members are contained in the set N.

Example:
N = {1 2 3 4 5 6}
if M = {1 2 3}, M is a subset of N.
if M = {1 2 7}, it would not be a subset of N, since 7 is not contained in N.
if M = {1 2 3 4 5 6}, M is still a subset of N.
if M = {3 2 5 6}, it is still a subset of N. Order does not matter in sets.

Answer 2

N might be the integers from 1 to 10:
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A subset of N (we could call it "O", say) might be the ODD integers between 1 and 10 (inclusive):
O = {1, 3, 5, 7, 9}

• All the members of O are also members of N, so O is a "subset" of N.

Another subset ("P", say) might be integers from 1 to 10 that are divisible by 7:
P = {7}

• P is a subset of O, and also of N.