List the elements of the following sets:
(1) {factor of 24}.
(2) {Negative integers greater than _9}.
(3) {Integers whose squares are less than 200 but greater than 40}.
(4) {Odd positive numbers less than 30}.
(Q2) Given that Y={multiples of 3 less than 20}, find the number of proper subsets of Y?
Q2: There are 6 members in Y: 3,6,9,12,15,18, so there are 2^6-2 = 62 proper subsets
surely you can handle the other items ...
#3 starts with
7^2 = 49
8^2 = 64
...
14^2 = 196
(1) The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
(2) The negative integers greater than -9 are: -8, -7, -6, -5, -4, -3, -2, and -1.
(3) The integers whose squares are less than 200 but greater than 40 are: -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13.
(4) The odd positive numbers less than 30 are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, and 27.
(Q2) To find the number of proper subsets of Y, we need to use the formula 2^n, where n represents the number of elements in the set.
Since Y is the set of multiples of 3 less than 20, we can count the number of multiples of 3 less than 20: 3, 6, 9, 12, 15, and 18.
Therefore, the number of proper subsets of Y is 2^6 = 64.
To find the elements of each set, we need to check the conditions given in the set.
(1) {factor of 24}:
The factors of 24 are the numbers that divide 24 without leaving a remainder. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
So, the elements of the set {factor of 24} are: {1, 2, 3, 4, 6, 8, 12, 24}.
(2) {Negative integers greater than -9}:
The negative integers greater than -9 are -8, -7, -6, -5, -4, -3, -2, and -1.
So, the elements of the set {Negative integers greater than -9} are: {-8, -7, -6, -5, -4, -3, -2, -1}.
(3) {Integers whose squares are less than 200 but greater than 40}:
To find the integers whose squares satisfy the condition, we need to find the integers whose squares fall between 40 and 200. The integers whose squares satisfy this condition are 7, 8, 9, 10, 11, 12, and 13.
So, the elements of the set {Integers whose squares are less than 200 but greater than 40} are: {7, 8, 9, 10, 11, 12, 13}.
(4) {Odd positive numbers less than 30}:
The odd positive numbers less than 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29.
So, the elements of the set {Odd positive numbers less than 30} are: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}.
(Q2) To find the number of proper subsets of Y={multiples of 3 less than 20}, we need to calculate 2^n - 1, where n is the number of elements in set Y.
The number of elements in set Y is the number of multiples of 3 less than 20, which are 3, 6, 9, 12, 15, and 18. So, n = 6.
Now, we can calculate the number of proper subsets using the formula: 2^n - 1.
Substituting n = 6, we have:
2^6 - 1 = 64 - 1 = 63.
Therefore, there are 63 proper subsets of Y.