Recent content by caws

  1. C

    Proof of 1^3 + 2^3 + ... n^3 = [n(n+1)/2]^2 for Positive Integers

    thanks, at least I know I am on the right track and was understanding the process, now all I have to do is solve to prove. :smile:
  2. C

    Proof of 1^3 + 2^3 + ... n^3 = [n(n+1)/2]^2 for Positive Integers

    Ok. I am going to try to work this through again and post tommorow.
  3. C

    Proof of 1^3 + 2^3 + ... n^3 = [n(n+1)/2]^2 for Positive Integers

    I am trying to prove by induction 1^3 + 2^3 + ... n^3 = [n(n+1)/2]^2 when n is a positive integer Let P(n), if P(1) then n^3 = 1^3 = 1 and [n(n+1)/2]^2 = [1(1+1)/2]^2 = 1 the inductive hypothesis is 1^3 + 2^3 + ... k^3 = [k(k+1)/2]^2 Assuming P(k) is true then prove P(k+1) is true...
  4. C

    Proving "If A U C = B U C then B = C" Without Drawing a Venn Diagram

    thanks all.. and also to HallsofIvy to the suggestion of making some simple sets. I submitted my homework and with the assigned variables and I received all points for this problem correctly.
  5. C

    Proving "If A U C = B U C then B = C" Without Drawing a Venn Diagram

    If I assign these elements Set A = {1} Set B = {1} Set C = {2} then assign it to my problem A U C = B U C then B = C A U C = {1, 2} B U C = {1, 2} which makes A U C = B U C true But B does not equal C since 1 does not equal 2 Is there a way to prove this without assigning...
  6. C

    Proving "If A U C = B U C then B = C" Without Drawing a Venn Diagram

    I am trying to prove this as false. Let A, B, C be any three sets. If A U C = B U C then B = C. I can draw a Venn Diagram to prove this and I can assign values to the sets to prove it, but how can I prove without doing this? Also is the counter value A U C = B U C then B not equal to C? Can...