Show that we can prove that P(n, k) is true for all pairs of positive integers n

Question:

Show that we can prove that P(n, k) is true for all pairs of positive integers n and k if we show
a) P(1, 1) is true and P(n, k) → [P(n + 1, k) ∧ P(n, k + 1)] is true for all positive integers n and k.
b) P(1, k) is true for all positive integers k, and P(n, k) → P(n + 1, k) is true for all positive integers n and k.
c) P(n, 1) is true for all positive integers n, and P(n, k) → P(n, k + 1) is true for all positive integers n and k.