Part b
Assuming the property holds for an arbitrary \(m \times n\) grid, prove that it also holds for a \((m+1) \times (n+1)\) grid using multi-parameter induction.
Strong Induction in Inequality Proofs
Using strong induction, prove that for all integers \( n \geq 5 \), the inequality \(2^n > n^2\) holds. In your proof, clearly state the base case and show how the inductive hypothesis is used to prove the statement for \( n+1 \).
Part b
Assuming the identity holds for \(n\) (i.e., \(\sum_{k=0}^{n} {n \choose k} = 2^n\)), prove that it holds for \(n+1\).