Step 1: Understanding the Concept:
Haemoglobin is a protein in red blood cells that transports gases between the lungs and the tissues.
Step 2: Detailed Explanation:
- Assertion: True. Haemoglobin is indeed the respiratory pigment in humans that carries oxygen to all cells.
- Reason: False. Haemoglobin has a very high affinity for oxygen, not carbon dioxide. Most carbon dioxide is transported in the dissolved form in blood plasma or as bicarbonates because \(CO_{2}\) is more soluble in water than oxygen is.
Step 3: Final Answer:
The assertion is correct, but the reasoning is biologically incorrect regarding the affinity of haemoglobin.