Recent content by setvectorgroup

I think what I did above looks a mess. I'd like to redo all that. Prove: If n is an integer such that n2 is even, then n is even. 1. Will this fly: Givens: n^2 is even (P) Goal: P- > Q I want to use the fact that not Q - > not P to get P - > Q New Given: not Q New Goal: not...

Thank You. Before I attempt the direct proof I'd like to know if what I wrote in c) passable as a proof, at least, conceptually? I mean is it correct, but ugly or incorrect and ugly? :smile:

Oh, I see about 2√12 ≠ √24. First I wrote √24, then 2√12. It should be 2√12.

Mark44, thank You for answering. 2*√6*√2 = √24? I think I forgot about this rule. Could you, please, tell me what rule that was? Can I use n^2 is even - > n = 2m, where m is any integer? As for c) not P: 1+ 6m = m^3- m where n is not a multiple of 6. To force n to be a non-multiple of 6...

Homework Statement Write down careful proofs of the following statements: a) sqrt(6)- sqrt(2) > 1 b) If n is an integer such that n^2 is even, then n is even. c) If n= m^3- m for some integer m, then n is a multiple of 6 The Attempt at a Solution I will rely on P - > Q and not...

Thank You, mfb.

If I were you, I'd read graduate texts without asking anyone's permission and stick around CC and play their games until I got my papers. In my experience, papers and money trump just about everything in this world.

Homework Statement Is the argument below valid? If it's valid, write down the argument symbolically. If a movie is not worth seeing, then it was not made in England. A movie is worth seeing only if critic Ivor Smallbrain reviews it. The movie The Good, The Bad and The Mathematician was...

Thank You, Pagan Harpoon.

Homework Statement "We say a set T is a subset of a set S if every element of T also belongs to S( i.e T consists of some of the elements of S). We write T ⊆ S if T is a subset of S and T ⊄ S if not. For example, if S = {1, {2}, cat}, then {cat} ⊆ S, {{2}} ⊆ S, 2 ⊄ S. As another example, the...

Well, I guess this does it. Thank You, ArcanaNoir, for (hopefully) closing this thread.

Thank You, vela. Here's yet another attempt to differentiate between 'element of' and 'subset of' (also, by subset I'll mean proper subset) :smile: Say, I got the following relations below and asked to see which ones are true, which ones- false: 2 ∈ {1,2,3} {2} ∈ {1,2,3} {2} ∈ {{1}, {2}}...

Thanks, Joffan, for the additional insight. What I wrote below might sound redundant, but I am trying to internalize all this set business: Is the notation above just a statement that two random sets happen to share the same elements while the set A also contains more of other elements...

That was very helpful, tiny-tim. I appreciate your help. :cool:

Thank You, tiny-tim. So, if {3, {3}} is a subset... Say, I make up a set S={1,2,3...}. Can I scoop up any collection of numbers from the set S and call it a subset? For example: T={1, 1000000000, 8} ⊂ S. Would that be right? edit: Also, if I were to modify the set A={b, {1,a},{3}, {{1,3}}...