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Kenneth Rosen Edition 7 Exercise 1.7 Question 38 (Page No. 92)
Pooja Khatri
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Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers
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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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Kenneth Rosen Edition 7 Exercise 1.7 Question 39 (Page No. 92)
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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Kenneth Rosen Edition 7 Exercise 1.4 Question 38 (Page No. 55)
Translate these system specifications into English where the predicate $S(x,y)$ is $x$ is in state $y$ and where the domain for $x$ and $y$ consists of all system and all possible states, respectively. $\exists x S(x, open)$ ... $\exists x \sim S(x, available )$ $\forall x \sim S(x, working)$
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