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Kenneth Rosen Edition 7 Exercise 1.7 Question 39 (Page No. 92)
Pooja Khatri
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Prove that at least one of the real numbers $a_1,a_2,...,a_n$ is greater than or equal to the average of these numbers.What kind of proof did you use?
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Pooja Khatri
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Kenneth Rosen Edition 7 Exercise 1.7 Question 42 (Page No. 92)
Prove that these four statements about the integer $n$ are equivalent: $n^2$is odd, $1−n$ is even, $n^3$ is odd, $n^2+1$ is even.
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Kenneth Rosen Edition 7 Exercise 1.7 Question 41 (Page No. 92)
Prove that if $n$ is an integer, these four statements are equivalent: $n$ is even, $n+1$ is odd, $3n+1$isodd, $3n$ is even.
Pooja Khatri
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Apr 4, 2019
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Kenneth Rosen Edition 7 Exercise 1.7 Question 38 (Page No. 92)
Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers
Pooja Khatri
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Apr 4, 2019
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Pooja Khatri
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Kenneth Rosen Edition 7 Exercise 1.5 Question 39 (Page No. 68)
Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers. $\forall x \forall y (x^2 = y^2 \rightarrow x =y)$ $\forall x \exists y (y^2=x)$ $\forall x \forall y (xy>=x)$
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