sort and concise answer and please use a mathematical perspective. thank you

Say whether the following statements are true or false. Be as rigorous as you can explaining your answers briefly. (a) "Only certain effects of the actions taken by other economic agents on a given agent should be called and analyzed as externalities." (b) "To determine the efficient level of national defense expenditure, one should equate the sum of all consumers' marginal rates of substitution between national defense and all other goods to the marginal cost of providing national defense." (c) "Suppose all consumers in the health insurance market are risk averse. There is a problem of the market equilibrium under asymmetric information, which consists of having many low-risk consumers choosing to opt out and not get insurance because it is too expensive, while in principle they should, given their risk aversion." (d) "In a general equilibrium exchange economy with ten identical con- sumers (i.e., same well-behaved preferences and endowments), there cannot exist Pareto efficient allocations where the utility levels of the different consumers are also different." (e) "If a technology exhibits increasing returns, it must necessarily be the case that, for at least one input, the marginal product is strictly increasing in the amount of that input.&quot