- #1
srfriggen
- 307
- 7
My book defines a proper subset: "a Set A is a proper subset of a set B if A [tex]\subseteq[/tex] B but A [tex]\neq[/tex] B. If A is a proper subset of B we write A[tex]\subset[/tex]B."
For example, S={4,5,7} and T={3,4,5,6,7}, then S [tex]\subset[/tex] T.
So, from my understanding, every element in S is contained in T however there is at least one other element in T not contained in S.
So what would an example of A[tex]\subseteq[/tex]B be?
My text says the [tex]N[/tex][tex]\subseteq[/tex][tex]Z[/tex] (Natural numbers and integers, respectively).
But every element of [tex]N[/tex] is contained in [tex]Z[/tex] and they are not equal, so wouldn't we write [tex]N[/tex][tex]\subset[/tex][tex]Z[/tex] ?
What would be an example of three sets A,B,C such that A[tex]\subseteq[/tex] B and B [tex]\subset[/tex] C ? (the notation is coming out funny looking for some reason... "A is a subset of B and B is a proper subset of C", is what I'm trying to say.
Would this be correct...
A={1,2,3}, B={1,2,3}, C={1,2,3,4} ?
Or would this be correct...
A={1,2,3}, B={{1,2,3}}, C={{1,2,3},4}
For example, S={4,5,7} and T={3,4,5,6,7}, then S [tex]\subset[/tex] T.
So, from my understanding, every element in S is contained in T however there is at least one other element in T not contained in S.
So what would an example of A[tex]\subseteq[/tex]B be?
My text says the [tex]N[/tex][tex]\subseteq[/tex][tex]Z[/tex] (Natural numbers and integers, respectively).
But every element of [tex]N[/tex] is contained in [tex]Z[/tex] and they are not equal, so wouldn't we write [tex]N[/tex][tex]\subset[/tex][tex]Z[/tex] ?
What would be an example of three sets A,B,C such that A[tex]\subseteq[/tex] B and B [tex]\subset[/tex] C ? (the notation is coming out funny looking for some reason... "A is a subset of B and B is a proper subset of C", is what I'm trying to say.
Would this be correct...
A={1,2,3}, B={1,2,3}, C={1,2,3,4} ?
Or would this be correct...
A={1,2,3}, B={{1,2,3}}, C={{1,2,3},4}