A disproportionation reaction is a specific type of redox reaction in which a single element is simultaneously oxidized and reduced. To identify which reactions are disproportionation reactions, let's analyze each option:
This is a disproportionation reaction because:
This reaction is also a disproportionation reaction:
This is not a disproportionation reaction because the oxidation states of manganese in the compounds involved do not simultaneously increase and decrease; instead, it involves a thermal decomposition and oxidation process.
This reaction involves redox changes but is not characterized as a disproportionation reaction as it involves separate species undergoing reduction and oxidation rather than a single element changing oxidation states in two directions within the same reaction.
Based on this analysis, the reactions that qualify as disproportionation reactions are (a) and (b). Therefore, the correct answer is (a) and (b) only.