Negative transitivity
The negative transitivity of a two-digit relation on a set is given if:
Strictly weak orders fulfill negative transitivity.
Equivalent transformations
Sometimes the connection of negative transitivity is formulated as follows:
This representation is obtained by negating an implication . If the expressions in brackets are replaced by the general statements A, B and C, it follows:
If this expression is negated again, firstly the direction of implication is reversed and secondly, according to De Morgan's laws, both the negations of A and B are canceled, but the conjunction is also transformed into a disjunction:
This then basically corresponds to the form we started from above.
Example in everyday language
If milk costs no less than bread and bread costs no less than cake, then milk costs no less than cake either.
Microeconomics
In microeconomic household theory , negative transitivity and asymmetry are used as assumptions for the strict preference relation .
See also
Individual evidence
- ^ Friedrich Breyer: Microeconomics: An introduction . Jumper; Edition: 5 ed. 2011 (September 25, 2011). ISBN 978-3642221491 . Page 166.
- ^ Friedrich Breyer: Microeconomics: An introduction . Jumper; Edition: 5 ed. 2011 (September 25, 2011). ISBN 978-3642221491 . Page 166.