What is wrong with this proof that integer solutions of n + 1 - k = 0 exist? Sup

Question

What is wrong with this proof that integer solutions of n + 1 - k = 0 exist? Suppose n = 7 and k = 8. Since k = n+1. Proving that n + 1 - k = 0. Nothing. "Since" introduces a subordinate clause, not a main clause. The subordinate clauses describes the reason for what follows in the main clause. Since k = n + 1, we have n + 1-k = 0."wouldhavebeen an acceptable phrase. We cannot use the-ing form for the main verb in a main clause. The word 'proving' suggests that what comes after that is supposed to be a concluding statement reiterating the theorem that has been proved. However, n + 1 - k = 0 is not the theorem: it's not even a proper statement, because k and n are undefined variables in that statement. What are n and k? Do they have values? Is this supposed to be true for all n and k? Or is merely the existence of integers n, k being asserted that make the equation true? Without that information, the equation is not a meaningful statement. A correct final conclusion would have been: "This proves that n + 1 - k = 0 has integer solutions n, k."

Explanation / Answer

Since in the statement n anh k are undefined variabls.

Therefore equation is not meanginful statement.

Hence option D is correct.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.