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...
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.
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...
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...