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...family, there are nodules (Figure 5), inside which live nitrogen-fixing bacteria of the rhizobia group. These bacteria fix about 108 tonnes of nitrogen per year worldwide, which is approximately 60% of all nitrogen fixed. This is a symbiotic relationship, with the bacteria providing the plant with nitrogen compounds, and the plant supplying nutrients to the bacteria....

...family TY of open sets defined in this way comprises a topology on Y. Answer We check (T1)–(T3). Since (T1)–(T3) are satisfied, TY is a topology on Y. So we have a bijection F:I(X) → Y between the topological spaces (I(X),Tf) and (Y,TY). Furthermore, from the definitions of open sets in Tf and TY, we can deduce immediately that for each U TY, F−1(U) Tf and for...

...family. You might have been able to add yet more detail (for example, mentioning the types of scale in the first track); you may even have recognised the interval between the two notes in the second track as a minor seventh (or at least, if you did not recognise the interval you should know that, with time, you could work it out). Naturally, the use of musical terminology...