Q/// irrational numbers is connected or disconnected in R

Q: Q/// rational numbers is connected or disconnected in R

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Q: 20. Prove: Let x and y be real numbers. If x is rational and y is irrational, then x + y is…

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

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

Q: If C = and C is symmetric, then b = -1 none of the above any real number ○ 1

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Q: Prove or disprove if x2-1 is odd, then x is even

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Q: 5. a. For all real numbers x and y, if x is rational and y is irrational, then x + y is irrational

A: We prove it by contrapositive statement that for any two real numbers x and y, we will prove that if…

Q: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

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Q: Prove that the product of an irrational number and a nonzero rational number is irrational. (Explore…

A: The proof is by contradiction i.e indirect proof.

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

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Q: Use proof by contradiction to show that 2 is not a rational number. Note that you may use the…

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Q: a. If b is any nonzero real number, prove that |1/b| = 1/| b | . b. Prove that |a /b | = |a|/| b|…

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

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

A: To Prove: x is a rational number if and only if 2x-1 is a rational number.

Q: For any integer m and any real number x, if x is integer, then x]+[m-x] = m- 1. -. not an

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Q: 3. Prove or disprove: there exist rational numbers a and b such that a/b is irrational.

A: Suppose there exist rational numbers a and b such that a/b is irrational.

Q: If a , b are two rational numbers such that Va + vb is a rational number, then prove that Vab is…

A: We have given that , a  and  b are two rational numbers  such that  a + b  is a rational number. We…