Prove that R is an equivalence relation.
Neil Armstrong and Edwin "Buzz" Aldrin were the first human beings to walk on the moon. Imagine it is the year 5050, and countries have been sending people to the moon since 2050. Each country has named its Moon mission—names like alpha, beta, gamma, etc. These mission groups have been using nuclear reactor-based electricity to compensate for the endless nights on the moon. When needed, most hi-tech groups with cutting-edge nuclear technology share their electricity with other groups that possess more vulnerable reactors. This energy-sharing process helps to foster both humanity and relationships on the lunar surface.
Naturally, energy production strengthens bargaining power for other goods between the mission groups. If you're producing a large amount of power, you may be able to trade for food or water. One way to compare energy production is formulated using the mathematical equation: Where This equation is the ratio of energy production from mission compared to that of mission . However, one must keep in mind that bargaining power is relative. To see this, we consider a relation among pairs from M x M (all possible pairs of Moon missions). When two groups have an electricity production ratio that is equal to another two groups electricity production (for example, ), we consider groups () to have a relation (R) with the groups (and ). Using notation, we can say that () R () and ((), () ∈ M ◊ M) where M is a set of groups living on the moon.
Prove that R is an equivalence relation.
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