Question: A relation R on a set S is irreflexive, if and only if, for every x E S, (x, ax) & S. Show that if

A relation R on a set S is irreflexive, if and only if, for every x E S, (x, ax) & S. Show that if R is irreflexive and transitive, then it is also antisymmetric

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

A relation R on the set A is irreflexive if for every a elementof A, (a, a) NotElement R. That is, R is irreflexive if no element in A is related to itself. A relation R is called asymmetric if (a,...

A binary relation R on a set A is irreflexive if and only if, for every aA,(a,a)/R. 1. Which relations in Exercise 2.19 are irreflexive? 2. Can a binary relation be neither reflexive nor...

Which relations in Exercise 3 are irreflexive? A relation R on the set A is irreflexive if for every a A, (a, a) R. That is, R is irreflexive if no element in A is related to itself.

class Queue using no other data structures than Item, Boolean, int and Stack. The amortized running time of each Queue meth od must be constant. (Note that you may only use the Stack as a black box:...

Determine whether the relation R on the set of all integers is reflexive, irreflexive, symmetric, antisymmetric, and/or transitive, where (x, y) is in R if and only if: A. x does not equal y...

A relation R on a set A is called irreflexive if for all a A, (a, a) R. (a) Give an example of a relation R on Z where R is irreflexive and transitive but not symmetric. (b) Let R be a nonempty...

3. 617 points| Pravibus Answers Determine whether the relation R on the set of all integers is reflexive, irreflexive, symmetric, antisymmetric, and/or transitive, where (x, y) is in R if and only if...

Teration 8 Show that the relation R in the set A 1 2 3 4 5 given by R a b ab is even is an equivalence relation Show that all the elements of 1 3 5 are related to each other and all the elements of 2...

Exercise 1: Example: A -(, 2), B f a, b) AX B ((, a), (1, b). (2, a). 2, b) Solve the following X; {a, c} and Y-(a, b, e, f). Write down the elements of (a) Xx Y- (d) What could you say about two...

A strict partial order on a finite set of elements S, is a binary relation that is irreflexive, anti- symmetric, and transitive. (These properties of relations are assumed to be background knowledge....

A pressure cooker has the lid screwed on tight. A small opening with A = 0.0075 in2 is covered with a petcock that can be lifted to let steam escape. How much mass should the petcock have to allow...

Distinguish among surveys, experiments, and observational methods of primary data collection. Cite examples of each method.

1 . Does high income guarantee financial security? Why or why not? 2 . How can people get more out of their money? 3 . If you were saving for a down payment on a house or the education of a child,...

The following table shows a sample of room rates for a 100 room resort hotel in Nova Scotia for the time period Jan.1 to Dec. 2003. Note that 1/1-7/3 means January 1 to March 7, 2003. Be sure to...