False

Explanation:

1. Contribution to Greenhouse Gas Emissions:
Agriculture is a significant contributor to greenhouse gas emissions, including methane. Methane is a potent greenhouse gas that is released during various agricultural activities. These activities include enteric fermentation in livestock, rice cultivation, and the management of organic waste.

2. Methane Emissions from Livestock:
Livestock, particularly cattle, produce methane through a process called enteric fermentation. Microorganisms in the digestive system of ruminant animals, such as cows and sheep, break down the fibrous materials in their diet and produce methane as a byproduct. This methane is then emitted through belching and flatulence.

3. Methane Emissions from Rice Cultivation:
Rice cultivation also contributes to methane emissions. When rice fields are flooded, anaerobic conditions are created, which promote the growth of methane-producing microorganisms. These microorganisms decompose organic matter in the flooded soil and release methane into the atmosphere.

4. Methane Emissions from Organic Waste Management:
The management of organic waste, such as manure and agricultural residues, can also lead to methane emissions. When organic waste decomposes under anaerobic conditions, methane is produced as a byproduct. This can occur in animal waste management systems, landfills, and composting facilities.

5. Overall Impact:
The contribution of agriculture to methane emissions is significant. Methane is a potent greenhouse gas, with a much higher global warming potential than carbon dioxide over a shorter timescale. Therefore, reducing methane emissions from agricultural activities is crucial in mitigating climate change.

Conclusion:
Contrary to the statement, agriculture does contribute to the production of greenhouse gases, particularly methane. The emissions from livestock, rice cultivation, and the management of organic waste all contribute to agricultural methane emissions. It is important to implement sustainable agricultural practices and technologies to reduce these emissions and mitigate climate change.