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!!!
