Your sentence does not make sense because it lacks the subject: what is equal to each other?. And when you say $xRx$, I'll ask you: what is $x$? Do you mean $xRx$ holds for some unspecified $x$, for all $x$, for some specific $x$? What set does $x$ range over?leigh ramona said:So reflexive is equal to each other. Like x R x.
This sentence is also problematic. For each $x$ and $y$, $xRy$ is either true or false. What do you mean by $xRx=yRx$? For which $x$ and $y$?leigh ramona said:Symmetric is x R y = y R x
This would be correct if you added "for all $x$, $y$ and $z$".leigh ramona said:Transitive is if x R y and y R z, then x R z.
What you wrote is true, but what does this have to do with $R$? Please enclose formulas in dollar signs: \$A\cap C\$.leigh ramona said:The relation is symmetric because if A \cap C = B \cap C, then C \cap A = C \cap B. Is this correct?
This does not makes sense because $A\cap C$ cannot be true or false: it's a set. Therefore, you can't write "If $A\cap C$...".leigh ramona said:The relation is also transitive, because if A \cap C and B \cap C, then A \cap B.
A relation R on a set U is reflexive if every element in U is related to itself, i.e. (a,a) ∈ R for all a ∈ U.
To prove that R on P(U) is reflexive, we need to show that for every subset A ∈ P(U), (A,A) ∈ R. This can be done by using the definition of reflexive relation and substituting A for a in the definition.
A relation R on a set U is symmetric if for any elements a and b in U, (a,b) ∈ R implies (b,a) ∈ R.
To prove that R on P(U) is symmetric, we can show that if (A,B) ∈ R, then (B,A) ∈ R for any subsets A and B in P(U). This can be done by using the definition of symmetric relation and substituting A and B for a and b in the definition.
A relation R on a set U is transitive if for any elements a, b, and c in U, if (a,b) ∈ R and (b,c) ∈ R, then (a,c) ∈ R.
To prove that R on P(U) is transitive, we can show that if (A,B) ∈ R and (B,C) ∈ R, then (A,C) ∈ R for any subsets A, B, and C in P(U). This can be done by using the definition of transitive relation and substituting A, B, and C for a, b, and c in the definition.