daphnevlogs11
08.08.2019 •
Mathematics
8. let r be the relation on the set of all sets of real numbers such that srt if and only if s and t have the same cardinality. show that r is an equivalence relation. what are the equivalence classes of the sets {0, 1, 2) and z?
Solved
Show answers
More tips
- F Food and Cooking How to Make Delicious Cabbage Pies: The Best Recipes!...
- S Science and Technology The Metric System in Our Daily Life: Understanding Its Importance...
- H Health and Medicine Angina: Causes, Symptoms, and Treatment...
- C Computers and Internet How to Learn to Type Fast?...
- F Food and Cooking Delight for Gourmets: How to Prepare Liver Pate...
- S Style and Beauty How to braid friendship bracelets?...
- H Health and Medicine Mercury Thermometer Danger: What to do when a thermometer breaks?...
- F Food and Cooking Which Calamari Salad is the Most Delicious?...
- S Society and Politics 10 Tips for Boosting Your Self-Esteem...
- F Food and Cooking The Most Delicious and Simple Fish in Batter Recipe...
Answers on questions: Mathematics
- M Mathematics 4. What is the x-intercept of 4y - 9x = 72?...
- M Mathematics With these: 18/36 = 1/? missing number change 1 5/8 to improper fraction. change 19/5 to a mixed number....
- M Mathematics What are the constants in this expression? -10.6+9/10+2/5m-2.4n+3m...
- M Mathematics Answer this 30 points and brainliest!...
- M Mathematics Find the sum of the measure of the interior angles of a polygon of 9 sides ; of 32 sides...
- M Mathematics The diameter of a ball is 8 in. what is the volume of the ball? use 3.14 for pi. enter your answer as a decimal in the box. round only your final answer to the nearest hundredth....
- M Mathematics Which is the graph of the function y=2(4)^x...
- M Mathematics Abiologist is recording the loss of fish in a pond. he notes the number of fish, f, in the pond on june 1. on july 1 there were 63 fish in the pond, which is 52 fewer fish than were...
- M Mathematics Suppose a ball is dropped fromca height of 6ft. it bounces back up but time it bounces, it reaches only 7/10 of its pervious height. what is the total of each height that the ball...
- M Mathematics Which sum or difference identity would you use to verify that cos (180° - ∅) = -cos ∅? a. sin (α -β) = sin α cos β – cos α sin β b. cos (α -β) = cos α cos β – sin α sin β c. cos (α...
Ответ:
We must prove that the relation is reflexive, symmetric and transitive. Recall that to sets have the same cardinality if there exist a bijective mapping between them.
Reflexive: Take the identity map , which is bijective. Then SRS.
Symmetric: If SRT then, there exist a bijective map . In order to prove that TRS just take the inverse map of : which is also bijective. Therefore, TRS.
Transitivity: Suppose that SRT and TRU. Also, assume that is the bijective map between S and T, and the bijective map between T and U. It is not difficult to check that the map is bijective and . Therefore, SRU.
Hence, the relation R is an equivalence relation.
The equivalence class of the set {0,1,2} is the class of all the sets with three elements, and we can associate it with the number 3. There is a construction of natural numbers based on this idea.
The equivalence class of Z is the same equivalence class of N. Therefore, is the class of all denumerable or countable sets.
Step-by-step explanation:
When we want to prove that a given relation R is equivalence, we need to check that R satisfies all the three conditions: reflexive, symmetric and transitivity. Usually the first two are very simple to prove and comes directly from the definition. The transitivity is more tricky. In this case we need to recall the definition of cardinality.
Ответ:
ya!!!
Step-by-step explanation:
thanks that's very generous