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Shown below are the steps of a proof by contraposition of the statement "If n is an integer and 5n + 3 is odd, then n is even." Match each step with its explanation.1. Assume n is not even, that is, it is odd. 2.Then n = 2k + 1 for some integer k. 3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) 4. Hence, 5n + 3 is even. Negation of the conclusion Definition of an odd integer Definition of an even number Arithmetic


Let's go over the correct explanation of each step. First, we assume that n is not even, which means it is odd - this is simply the negation of the conclusion. We can then use the definition of an odd integer to deduce that n must equal 2k + 1 for some integer k. Now, what is the contraposition of this statement? When we are familiar with the inverse statement, it becomes easy to construct a contrapositive statement. We simply take the negation of the hypothesis and the conclusion to produce the opposite of the conditional statement. After creating the inverted statement, we swap the hypothesis and conclusion to create the contrapositive of the conditional statement. Applying this logic, we notice that 5n + 3 can be simplified to 5(2k + 1) + 3, which simplifies further to 10k + 8. This simplification reveals that 5n + 3 is, in fact, an even number. For further information on this topic, feel free to visit brainly.com/question/25211275 #SPJ4.