That same question is answered here.
http://www.mathhelpforum.com/math-he...l-algebra.html
for the question: Assume that R and S are relations on a set A. Prove
(using relation-algebraic calculations) or disprove (by providing
counterexamples) each of the following statements.
a) If R and S are both reflexive, then R ∪ S is reflexive, too.
how would i start to answer this question its the syntax of the answer iam having trouble with
This is what i have R U S = R Subset of S = A<=>A subset of S = Id A subset of S therefore reflexive
That same question is answered here.
http://www.mathhelpforum.com/math-he...l-algebra.html
hi thanks for the answer that the answer i got but you can't just give the answer with out some explanation.
A<=>A is =: P(AXA)
Subset of =: C
Identity A =: Ia
And =: ^
composed of =: o
This is what i did
R: A<=>A its definition of reflexive for this is Ia C R
S: A<=>A its definition of reflexive for this is Ia C S
(Ia C R) ^ (Ia C S)
(Ia ^ Ia) C (R ^ S)
(Ia) C (R ^ S )
So therefore (Ia) C (R intersect S)
The question is would i change the or into an intersection or a unison because i remember that unison has the same shape as or and Intersect has the same shape as Or so why in this case does this work or why doesn't it work
again are there any references anywhere for this material
Question number 2
R and S are both reflexive then R o S is reflexive
So i start the same way.
R: A<=>A its definition of reflexive for this is Ia C R
S: A<=>A its definition of reflexive for this is Ia C S
(Ia C R) ^ (Ia C S)
Than what? i dunno what to do from this point if you guys can't help that's fine this is really difficult stuff and the resources don't really explain the material well i am hoping to write a book for this and for calculus level 1 and 2 in a way that is understandable with common misconceptions.