Of the 125 students in an elementary school, some only play checkers, some only play chess, and some play both. 89 students play checkers and 45 students play checkers and chess. How many students in the school play chess
If A = {2, 6, 10, 14, 18, 22, 26, 30} and B = {-6, -3, 5, 10, 16, 22, 30, 42}, what is A∩B?
Solve and graph (3x-2)/2-4 ≥10 or (2x+3)/3-2≤3
10) Identify all the subsets of {2, 9
A∩B means the set of elements that are common (or the same) in two sets: A and B. Sometimes you will have no elements that are the same between two sets and you will indicate this as {} meaning empty set. The symbol ∩ is known as intersection of two sets. You will set-up the problem as follows:
A = {2, 6, 10, 14, 18, 22, 26, 30} and
B = {-6, -3, 5, 10, 16, 22, 30, 42}
{2, 6, 10, 14, 18, 22, 26, 30} ∩ {-6, -3, 5, 10, 16, 22, 30, 42}
= {10, 22, 30}
I am assuming for #10 you want subsets of {2, 9}.
Let P(S) stand for Power Set of S,therefore your subsets will be
P(S) = P({2,9}) = {},{2},{9},{2,9}.
Sorry, forgot to put my name :)
A∩B means the set of elements that are common (or the same) in two sets: A and B. Sometimes you will have no elements that are the same between two sets and you will indicate this as {} meaning empty set. The symbol ∩ is known as intersection of two sets. You will set-up the problem as follows:
A = {2, 6, 10, 14, 18, 22, 26, 30} and
B = {-6, -3, 5, 10, 16, 22, 30, 42}
{2, 6, 10, 14, 18, 22, 26, 30} ∩ {-6, -3, 5, 10, 16, 22, 30, 42}
= {10, 22, 30}
I am assuming for #10 you want subsets of {2, 9}.
Let P(S) stand for Power Set of S,therefore your subsets will be
P(S) = P({2,9}) = {},{2},{9},{2,9}.
To find the number of students who play chess in the elementary school, we can use the principle of inclusion-exclusion.
Given:
Total students in the school (n) = 125
Students who play checkers (A) = 89
Students who play both chess and checkers (A ∩ B) = 45
To find the number of chess players (B), we can use the formula:
B = Total students - (A - A ∩ B)
Substituting the given values into the formula:
B = 125 - (89 - 45)
B = 125 - 44
B = 81
So, there are 81 students in the school who play chess.
For the second question, we need to find the intersection of sets A and B.
Set A = {2, 6, 10, 14, 18, 22, 26, 30}
Set B = {-6, -3, 5, 10, 16, 22, 30, 42}
The symbol for intersection is denoted as ∩. It represents the elements that are common to both sets.
To find A ∩ B, we need to identify the elements that appear in both sets A and B.
A ∩ B = {10, 22, 30}
So, the intersection of sets A and B is {10, 22, 30}.
For the third question, we have an inequality to solve and graph:
(3x - 2) / 2 - 4 ≥ 10 or (2x + 3) / 3 - 2 ≤ 3
To solve and graph the inequality, we can follow these steps:
Step 1: Solve the first inequality:
(3x - 2) / 2 - 4 ≥ 10
Multiply both sides of the inequality by 2 to eliminate the denominator:
3x - 2 - 8 ≥ 20
3x - 10 ≥ 20
Add 10 to both sides of the inequality:
3x ≥ 30
Divide both sides of the inequality by 3:
x ≥ 10
So, the solution to the first inequality is x ≥ 10.
Step 2: Solve the second inequality:
(2x + 3) / 3 - 2 ≤ 3
Multiply both sides of the inequality by 3 to eliminate the denominator:
2x + 3 - 6 ≤ 9
2x - 3 ≤ 9
Add 3 to both sides of the inequality:
2x ≤ 12
Divide both sides of the inequality by 2:
x ≤ 6
So, the solution to the second inequality is x ≤ 6.
Step 3: Combine the solutions from both inequalities:
We have x ≥ 10 and x ≤ 6. These two conditions cannot both be true simultaneously, so there is no solution that satisfies both inequalities.
Therefore, the system of inequalities has no solution.
Finally, for the fourth question, we need to identify all the subsets of the set {2, 9}.
A subset is a set that contains elements from a larger set. In this case, the larger set is {2, 9}.
The subsets of {2, 9} are:
1. The empty set (∅)
2. {2}
3. {9}
4. {2, 9}
So, the subsets of the set {2, 9} are ∅, {2}, {9}, and {2, 9}.