+1886 Let A={x∈N|x2<37} and B={3k+1|k∈{1,2,3,4}} be sets.
1. List the elements of A and B, and the subsets of B.
2. For any sets A, B, and C, prove or disprove the claim: If A∈B, B∈C, then A∈C.
3. Show {12a+4b|a,b∈Z}={4c|c∈Z}
+309 I assume N is for natural numbers and Z is for integers.
1.
A = {1, 2, 3, 4, 5, 6}
B = {4, 7, 10, 13}
Subsets of B are any combination of the elements of B (excluding some).
2.
If A is contained within B, and B is contained with C, A is contained within C.
This is, I suppose, one of those annoying proofs which I take for granted and see no way of prooving it other than it is logical. It is here I should also note that I have never studied set theory, and I'm probably getting everything wrong .
3.
{4(3a+b)|a,b ∈Z} = {4c|c∈Z}
{3a+b|a,b∈Z}={c|c∈Z}
3a+b∈Z
c∈Z
(I don't know what to do after that....)
Again, I've never studied this, so apologies in advance for faulty logic everywhere.
