Recent content by Willy_Will

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    Is A x B equal to B x A if and only if A equals B?

    Hi all... Homework Statement Let A, B be non-empty sets, proof that A x B = B x A iff A = B Homework Equations A x B = Cartesian Product iff = if and only if ^ = and The Attempt at a Solution Let (x,y) є A x B = B x A iff (x,y) є (A X B) ^ (x,y) є (B x A)...
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    Undergrad Is it true for all n, Natural number?

    Glad there is edit here... its late, I am not thinking straight. I didnt catch the counter example, sorry.
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    Undergrad Is it true for all n, Natural number?

    If you say no, why no? N = Natural numbers, thanks for your reply!
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    Undergrad Is it true for all n, Natural number?

    Interesting e(hoOn3... I was thinking something like that, other opinions?
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    Graduate Proving Properties of a Nested Family of Sets

    Hi all, Im having trouble with this problem, I don't know where to begin. Suppose that Ä is a nested family of sets. 1. Prove that U (from k=1 to infite) A(sub k) = A(sub l) 2. Prove that ∩ (from k=1 to n) A(sub k) = A(sub n) Thanks in advace mathematicians! -William
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    Undergrad Is it true for all n, Natural number?

    Hello all, Another quick question for the number theory gurus here: Let P(n) predicate, n Natural number. Suppose that P(n) satisfies that P(1) is true, and if k in N, P(k) is true, then P(k+2) is true. Is P(n) true for ALL n in N? Why? Thanks in advace guys! -William
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    Undergrad Pairwise disjoint set proof (help)

    Thanks guys!
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    Undergrad Pairwise disjoint set proof (help)

    if x and y are elements of T, then they are elements of D. because T is a subset of D. However, xny will be empty set, because they are also elements of D, and D is pairwise disjoint. T is also pairwise disjoint. Like that?
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    Undergrad Pairwise disjoint set proof (help)

    hello, I really don't know how to proceed here, since I don't know very much about sets/family. I want to prove that if Ð is a family of pairwise disjoint sets, and Ŧ is a subset of Ð, prove that Ŧ is also a family of pairwise disjoint sets. Thanks in advance math gurus William
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    Undergrad Divisibility problem cant use module just induction

    Thanks guys, I really appreciate it!
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    Undergrad Divisibility problem cant use module just induction

    sorry for the double post. (1) = (8^k - 3^k) (2) = (8 - 3) (1) by hypotesis 5 divides the expresion. (2) 5 = 8 - 3, 5 divides 5. = 8(5x) + 3^k(5) = 5(8x + 3^k) 5 divides the expresion
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    Undergrad Divisibility problem cant use module just induction

    I think I've got it. Suppose that 5 divides 8^k - 3^k ---> 8^k - 3^k = 5x, for some integer x. case n = k +1 = 8^k+1 - 3^k+1 = 8(8^k) - 3(3^k) = 8(8^k) - (3^k)(8) + (3^k)(8) - (3)(3^k) = 8(8^k - 3^k) + 3^k(8 - 3) (1) (2) (1) by hypotesis 5 divides the...
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    Undergrad Divisibility problem cant use module just induction

    I think I've got it. Suppose that 5 divides 8^k - 3^k ---> 8^k - 3^k = 5x, for some integer x. case n = k +1 = 8^k+1 - 3^k+1 = 8(8^k) - 3(3^k) = 8(8^k) - (3^k)(8) + (3^k)(8) - (3)(3^k) = 8(8^k - 3^k) + 3^k(8 - 3)...
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    Undergrad Divisibility problem cant use module just induction

    I think so, but how can I use that in my problem?
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    Undergrad Divisibility problem cant use module just induction

    Hi all, Great forum, I have been reading some cool stuff here for about a month. Heres my question: Using induction prove that 5 divides 8^n - 3^n, n Natural Number. I know its true for n = 1, but I get stuck on the n = k+1. I don't know how to proceed from here: 8(8^k) - 3(3^k)...