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Arbitrage free, is it dominance or value additivity


I haven’t been sure on how to differentiate between dominance or value additivity arbitrage. At first I thought it is as simple as just checking whether we need to (for example buy multiple bonds and see one/multiple bonds). I thought dominance would be the case only when two bonds have different prices. However, question 11 in the book in The Arbitrage-Free Valuation Framework has got me confused as they considered that arbitrage dominance as the discount rates are different. I mean discount rates will be always different even with value additivity. 

What’s the way you use to check whether it is value additivity or dominance? 

If you could check that question. It can also be value additivity by combining 2 bonds of A


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Your concept would be correct if they have used sum of a parts, but if i remember in this cases they had two (different) assets

and the main problem here that these two assets were risk free and according to their present value it seems that they are discounted using different discount rates which is an arbitrage profit according to dominance principle.