Using strong induction (so, neither weak nor "weak++") on the number of matches in the pile, prove that if this number is of the form 4k + 1, for k ∈ N, then P2 always has a strategy to win (which they will follow, because they are smart). Otherwise, P1 always have a strategy to win (which they will also follow because they’re smart too)! To be clear, you will need to prove both facts with a single inductive proof! That is to say, you will need to prove that P2 can always win under the aforementioned condition, but whenever that condition is not met, you have to prove that it is now P1 that can always win!

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.

did u ever get the answers? i need