Sign In
Ask Question
Reina Duran
Mathematics
8 January, 02:14
Prove that
For all sets A and B, A∩ (A∪B) = A.
+1
Answers (
1
)
Genevieve Hoover
8 January, 02:25
0
A∩ (A∪B) = A
Step-by-step explanation:
Let's find the answer as follows:
Let's consider that 'A' includes all numbers between X1 and X2 (X1≤A≥X2), and let's consider that 'B' includes all numbers between Y1 and Y2 (Y1≤B≥Y2). Now:
A∪B includes all numbers between X1 and X2, as well as the numbers between Y1 and Y2, so:
A∪B = (X1≤A≥X2) ∪ (Y1≤B≥Y2)
Now, A∩C involves only the numbers that are included in both, A and C. This means that 'x' belongs to A∩C only if 'x' is included in 'A' and also in 'C'.
With this in mind, A∩ (A∪B) includes all numbers that belong to 'A' and 'A∪B', which in other words means, all numbers that belong to (X1≤A≥X2) and also (X1≤A≥X2) ∪ (Y1≤B≥Y2), which are:
A∩ (A∪B) = (X1≤A≥X2) which gives:
A∩ (A∪B) = A
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Find an answer to your question 👍
“Prove that For all sets A and B, A∩ (A∪B) = A. ...”
in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in
What is 10x224 and how was your day
Answers (1)
Are all angles of a parallelogram congruent (always, sometimes, or never)
Answers (1)
Ben and Antonio both take the same bus to school. Ben's ride is 7/8 mile. Antonio's ride is 3/4 mile. Who has a longer bus ride?
Answers (2)
Jerome's sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio of water to drink mix the same and still increase the total amount of energy drink.
Answers (1)
Kedre wants to know the average height of soccer players at her school. She randomly surveyed 12 soccer players. Her data is below.
Answers (1)
New Questions in Mathematics
What is a random variable
Answers (1)
You are making punch for a team party using 3 liquids. You combine 2gallons and 3 quarts of fruit punch, 1gallon and 2 quarts of pineapple juice, land 3 gallons and 3 quarts of orange juice.
Answers (1)
store one is selling three notebooks for $5.13 store to is selling 5 notebooks for $8.40 store 3 7/8 notebooks for $14 in which store are the notebooks the cheapest
Answers (1)
If 38 is added to 5/9 of a number, the result is 88. find the number. a) 10 b) 90 c) 50 d) 80
Answers (1)
Dezi says that there are more ounces in 1 ton than there are pounds. Do you agree? Explain
Answers (1)
Home
»
Mathematics
» Prove that For all sets A and B, A∩ (A∪B) = A.
Sign In
Sign Up
Forgot Password?