Find the error in the \"proof\" of the following \"theorem\". \"Theorem\": Let R

Question

Find the error in the "proof" of the following "theorem".
"Theorem": Let R be a relation on a set A that is symmetric and transitive. Then R is reflexive.

"Proof": Let a be an element of A. Take an element b that is an element of A such that (a,b) is an element of R. Because R is symmetric, we also have (b,a) is an element of R. Now using the transitive property, we can conclude that (a,a) is an element of R because (a,b) is an element of R and (b,a) is an element of R.


Please SHOW all your WORK. and EXPLAIN very thoroughly how you came at your answer. Give me step by step how you got your answer.

Explanation / Answer

Find the error in the "proof" of the following "theorem".
"Theorem": Let R be a relation on a set A that is symmetric and transitive. Then R is reflexive.

"Proof": Let a be an element of A. Take an element b that is an element of A such that (a,b) is an element of R. Because R is symmetric, we also have (b,a) is an element of R. Now using the transitive property, we can conclude that (a,a) is an element of R because (a,b) is an element of R and (b,a) is an element of R.


Please SHOW all your WORK. and EXPLAIN very thoroughly how you came at your answer. Give me step by step how you got your answe

A WILL ALSO BE PERPENDICULAR TO B

SO WE HAVE A IS RELATED TO B AND B IS RELATED TO A...

BUT TO SAY THAT HENCE 

A IS RELATED TO A OR B IS RELATED B IS ABSURD,

SINCE THEN IT NEEDS A TO BE PERPENDICULAR IT SELF AND

B TO BE PERPENDICULAR TO IT SELF!!

HENCE THE MORAL IS THAT WE SHOULD HAVE 3 DISTINCT ELEMENTS 

A,B AND C SATISFYING A TRANSITIVE PROPERTY AND NOT JUST 2 ELEMENTS

A AND B .....

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