Question

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Answer 1

Answer:

c) If natural numbers are regarded as positive whole numbers only

C = {7n|n∈N, n<5} = {7, 14, 21, 28}

If natural numbers are regarded as non-negative integers

C = {7n|n∈N, n<5} = {0, 7, 14, 21, 28}

d) D = {3n|n∈W} = {0, 3, 6, 9, 12, ...}

Note that the three dots at the end indicate that the set is infinite.

e) E = {all possible remainders from division of a natural number by 6} = {0, 1, 2, 3, 4, 5}

Step-by-step explanation:

Complete Question

List all elements of each set. (Note that sometimes you will have to put three dots at the end, because a set is infinite.)

c) C = {7n|n∈N, n<5}

d) D = {3n|n∈W}

e) E = {all possible remainders from division of a natural number by 6}

Solution

c) Note that C = {7n|n∈N, n<5} means that we write a set of numbers 7n, given that n is a natural number and is less than 5.

A natural number is defined as positive whole number or a non-negative integer.

If we take natural numbers and positive whole numbers, n that will satisfy this question include 1,2,3 and 4.

7n = 7, 14, 21 and 28

C = {7n|n∈N, n<5} = {7, 14, 21, 28}

If you regard natural numbers as just non negative integers, n = 0,1,2,3 and 4.

7n = 0, 7, 14, 21 and 28

C = {7n|n∈N, n<5} = {0, 7, 14, 21, 28}

d) Note that D = {3n|n∈W} means a set of numbers, 3n, given that n is a whole number.

Whole numbers start from 0,1,2,3,4..... till infinity.

n = 0,1,2,3,4,..

3n = 0, 3, 6, 9, 12, ...

D = {3n|n∈W} = {0, 3, 6, 9, 12, ...}

Note that the three dots at the end indicate that the set is infinite.

e) E = {all possible remainders from division of a natural number by 6}

The possible remainders when a natural number is divided by 6 include 0, 1, 2, 3, 4 and 5. Hence,

E = {all possible remainders from division of a natural number by 6} = {0, 1, 2, 3, 4, 5}

Hope this Helps!!!