Recall that a polynomial-time reduction from problem A to problem B (A ≤ₚ B) means that we can solve A by transforming its input into an input for B and using B's solution, all within polynomial time.

To prove transitivity, assume A ≤ₚ B and B ≤ₚ C, then construct a reduction from A to C by composing the two given reductions, ensuring the composition remains polynomial-time.

Demonstrate that the composition of the two reductions (A → B and B → C) results in a valid reduction A ≤ₚ C by carefully analyzing the polynomial-time complexity of the composed transformation.