In this section, we noted that the relations \"is equal to\" and\"is congruent t

Question

In this section, we noted that the relations "is equal to" and"is congruent to" are reflexive, symmetric, and transitive. Therelation "is a cousin of" is symmetric but neither reflexive nortransitive. Give an example of a relation (mathematical ornonmathematical) that is a. reflexive and symmetric but not transitive b. symmetric and transitive but not reflexive c. reflexive and transitive but not symmetric In this section, we noted that the relations "is equal to" and"is congruent to" are reflexive, symmetric, and transitive. Therelation "is a cousin of" is symmetric but neither reflexive nortransitive. Give an example of a relation (mathematical ornonmathematical) that is a. reflexive and symmetric but not transitive b. symmetric and transitive but not reflexive c. reflexive and transitive but not symmetric

Explanation / Answer

QuestionDetails: In this section, we noted that the relations "is equal to" and"is congruent to" are reflexive, symmetric,
and transitive. The relation "is a cousin of" is symmetricbut neither reflexive nor transitive.
Give an example of a relation (mathematical ornonmathematical) that is a. reflexive and symmetric but not transitive
CONSIDER THE RELATION..|A-B|<=1
IT IS REFLEXIVE SINCE |A-A|<=1
IT IS SYMMETRIC SINCE IF |A-B|<=1 THEN |B-A|<=1
IT IS NOT TRANSITIVE SINCE |A-B|<=1 AND |A-C|<=1...DOE NOTIMPLY |A-C|<=1
FOR EX. A=5,B=4,C=3
b. symmetric and transitive but not reflexive
CONSIDER THE SET [1,2,3] WITH RELATION[(1,2);(2,1);(1,3);(3,1);(2,3);(3,1)]
IT IS SYMMETRIC SINCE FOR TWO ELEMENTS 2 AND 3 IN THE SET
BOTH (2,3) AND (3,2) ARE IN RELATION.
IT IS TRANSITIVE SINCE FOR THREE ELEMENTS 1 , 2 AND 3IN THE SET.
SINCE (1,2) AND (2,3) IMPLIES (1,3) IN THE RELATION ETC HOLDSGOOD
FOR ALL THREE ELEMENTS IN THE SET.
IT IS IS NOT REFLEXIVE AS YOU CAN SEE NONE OF THE ELEMENTS
1 OR 2 OR 3 HAVE (1,1);(2,2);(3,3) IN THE RELATION.
c. reflexive and transitive but not symmetric
CONSIDER THE RELATION A<=B
IT IS REFLEXIVE SINCE A<=A
IF A<=B AND B<=C....THEN ....A<=C.....SO TRANSITIVE.
BUT IF A<=B...THEN...B<=A IS NOT ALWAYS TRUE.

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