Log In
0 votes
What is the covering relation of the partial ordering {(A, B) | A ⊆ B} on the power set of S, where S = {a, b, c}?

i’m getting

R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, {b, c}), ({b}, {a, b}), ({c}, {b, c}), ({a}, {a, b}), ({a}, {a, b, c}), ({b}, {a, b, c}), ({c}, {a, b, c}), ({a, b}, {a, b, c}), ({b, c}, {a, b, c}), ({a, c}, {a, b, c}) }

but in Rosen answer gives is

(∅, {a}), (∅, {b}), (∅, {c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, {a, b}), ({b}, {b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
in Set Theory & Algebra 120 views
according to definition,
subset B covers subset A when you add only one element to subset A which is not in A.
if you write ( $\phi$, {a, b}) then $\phi \subseteq \{a\} \subseteq \{a, b\} $ or $ \phi \subseteq \{b\} \subseteq \{a, b\} $ which is violating the definition of covering relation.
So,  for every pair, add only one element in B which is not in A (or)  make the hasse diagram and then check.
can u pls refer the definition of covering relations
I didn't find it in Rosen
thank u

Please log in or register to answer this question.

Related questions

0 votes
1 answer
Suppose that $A$ is a nonempty set, and $f$ is a function that has $A$ as its domain. Let $R$ be the relation on $A$ consisting of all ordered pairs $(x, y)$ such that $f (x)=f (y)$ $a)$ Show that $R$ is an equivalence relation on $A$ $b)$ What are the equivalence classes of $R?$
asked Apr 23, 2019 in Set Theory & Algebra aditi19 97 views
1 vote
0 answers
Let R be the relation on the set of functions from $Z^+$ to itself such that (f,g) belongs to R iff f is $\Theta(g)$ The equivalence class of f(n)=$n^2$ is set of all functions who are in $\Theta(n^2)$ is it correct?
asked Jun 30, 2018 in Set Theory & Algebra Ayush Upadhyaya 75 views
0 votes
0 answers
Given below is a table where R is a relation having pairs (x,y) over the set of real numbers and these ordered pairs will be in R if and only if the condition given on the left most side of the table is satisfied. The various columns represent ... relation can have R-Reflexive IR-Irreflexive S-Symmetric ATS-Anti-symmetric AS-Asymmetric T-Transitive. Let me know if below table entries are correct.
asked Jun 29, 2018 in Set Theory & Algebra Ayush Upadhyaya 97 views
1 vote
0 answers