1

I know that given an at most k out of N tool I can get an at least K out of N by changing it to at most (n-k) out of N.

But I can't seem to wrap my head around how this is true. I might be missing something very trivial

For example, if K=2 and N=6 how is at least 2 out of 6 equivalent to at most 4 out of 6

any help would be appreciated

lava_07
  • 83
  • 1
  • 7

1 Answers1

2

As you put it, the equivalence just isn't true. So, don't feel bad about not understanding it. To see, let's take an example. Let's say we have booleans only, N=6 and K=2, and the assignment:

True False False False False False

to these 6 variables. The statement At most 2 out of 6 are True is obviously satisfied by this assignment, but At least 4 out of 6 are True is not.

Maybe what you meant is:

at least K out of N is True

is equivalent to

at most N-K out of N is False

which can be further generalized to say:

at least K out of N objects have property P

is equivalent to:

at most N-K out of N objects do not have the property P

Is this what you were trying to express? Hope that's more clear!

alias
  • 28,120
  • 2
  • 23
  • 40