The Problem says:
My difficulty is I do not understand the question. I was able to complete the first two. I do not know what it means by "The relation ⊆ on a set of sets." I used the power set because I thought where A ⊆ B it was asking for the ordered pair {A,B}.
Then on the relation ⊆ on a set of sets (considering the set {{a},{b},{c}}), relations should be nonrelfexive, nonsymmetric, transitive, and Antisymetric.
Relations are not irreflexive or intransitive.
I think they are also not asymmetric because of <{{a},{b},{c}} , {{a},{b},{c}}> where...
Yes, φ is the power set.
I have changed these to reflect what I believe is accurate but still have trouble with number 5.
G = {{b},{c},d,{∅}}
1) {{c}} ⊆ G
2) {b} ⊈ G
3) {d} ⊆ G
4) d ⊈ G
5) ∅ ⊆ G – would the empty set be a subset of G? I know {∅} is an element G, but ∅ is still a set.
6) c \in...
Homework Statement
Determine whether the relations on three sets are Reflexive, Irrelfexive, Symmetric,, Asymmetric, Antisymmetric, Transitive, and Intransitive.
The relation \subseteq on a set of sets.
Homework Equations
The Attempt at a Solution
I am having trouble figuring out...
For the set G where G = {{b},{c},d,{∅}}, I believe these are correct:
1) {{c}} \subseteq G
2) {b} \subseteq G
3) {d} \subseteq G
4) d \subseteq G
5) ∅ \subseteq G
6) c \notin \varphi(G)
7) {c} \in \varphi(G)
8) {b} \subseteq \varphi(G)
9) {{d}} \notin \varphi(G)
10) ∅ \in \varphi(G)...