Prove or disprove each of the following statements. To disprove just give a counter example. If n is an even positive integer, then 3n+2"-² is even. 8x-1 x²+4 Every nonzero rational number can be written as the product of four irrational numbers. If f(x) = " then f is one to one.

Q: - 10 +V-175 al expression 5 er in exact form without decimals. To enter a on

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A: We will prove r -s is rational number by direct proof as shown below

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A: Given: Given statement is The quotient of any two rational number is rational number.

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Q: Number 4 only. Thanks!

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A: we say a number is rational when it is in p/q form where p≠0.

Q: y = ||

A: The general equation of the harmonic function is y=6*cos(a*x).

Q: упе y ne N.

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Q: Number 2 only. Thanks!

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Q: 6. Prove that x is a rational number if and only if 2x – 1 is a rational number.

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Q: If n is a positive integer, then 2 n - [a] »] + [a + ²] + [a + ² ] -- - + [a + ¹ = ¹] - =] = n n =…

A: Given: nis a positive integer. To Prove: α+α+1n+α+2n . . . +α+n-1n=nα

Q: 7 [3-(2-5x)] + X= 4 (9x+2} +1+x/²

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Q: (b) Consider the following set of real numbers 2n 4-{²₂²REN} :ne n+2 A = Answer the following…

A: We have to find the supremum of

Q: Prove the following statement directly from the definition of rational number. The difference of any…

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Q: There exists a real number R which is greater than 5 O R= {7, 42,2t, and 97/3) O R= {1, 2, and T/6}

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Q: 2. For each of the following, use a counterexample to prove the statement is false. * (a) For each…

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