If x has k elements, than Y has n-k to n-k elements at most!
Minimum value for k is 1, and max is n-1
It's pretty much pointless to write about 2 elements since that way I'd have only 2 cartesian products only since by the condition sets are not subsets so they can't be equal to the parent ie...
Set S with n elements!
Set size of
{<x,y> | (X,Y are proper subsets of S), (X union Y = S)!
I tried doing something, but I'm stuck staring at a closed door, so I need a fresh start!
Any hints would be appreciated!
Got it now :) let's denote the initial statement as K + L, so we have sth like 24l + 7k = 7(k+l) + 17k, sum of two numbers divisible by 17 is divisible by 17, anyway thx
I proved the base case n=1, and then I try doing the step case assuming that it satisfies for any k, then I try proving it by k+1.
I got sth like 24 * (3 * 5^(2k+1)) + 7 * 2^(3k +1) Now I'm stuck can't continue, I don't have any ideas :/
btw the initial equation is 3 * 5^(2n+1) + 2^(3n+1) !