Transitivity property not clear.

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SUMMARY

The discussion centers on the transitivity property of equivalence relations as defined in mathematical terms. Specifically, it states that for any three elements a, b, and c in a set X, if a is related to b and b is related to c, then a must also be related to c. The participants confirm that upon examining all combinations of a, b, and c, the transitivity property consistently holds true, reinforcing its validity in equivalence relations.

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  • Understanding of equivalence relations
  • Familiarity with mathematical notation and logic
  • Basic knowledge of set theory
  • Ability to analyze logical statements
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  • Study the formal definition of equivalence relations in set theory
  • Explore examples of transitivity in various mathematical contexts
  • Learn about other properties of equivalence relations, such as reflexivity and symmetry
  • Investigate applications of equivalence relations in computer science, particularly in algorithms
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Mathematicians, computer scientists, students studying discrete mathematics, and anyone interested in understanding the properties of equivalence relations.

lalapnt
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i am reading equivalence relation on wikipedia. and in this examply. i don't see the transitity property according to the definition of transitivity which is: For every three elements a, b, and c in X, if a ~ b and b ~ c, then a ~ c (transitivity).

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any explanation please?
 
Physics news on Phys.org
If you go through all possible combinations of a, b, and c for which a~b and b~c hold, you will find that a~c also holds in all these cases.
 

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