Let A be the set of irrational numbers in [0, 1] and let B be the set of ratinal numbers in [0, 1]. a) Show that m*(B) = 0. b) Show that m*(A) = 1.

Q: Show that if x, y are rational numbers, then x + y and xy are rational numbers.

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Q: Derive one-one correspondence between the real numbers in (0,1) and the set of irrational numbers in…

A: Both the sets that is real number in 0,1 and the set of irrational numbers in 0,1 are uncountable as…

Q: Let a,b,c,d be real number with a < b < c < d. Express the set [a,b] U [c,d] as the difference of…

A: We have given that, a, b, c, d are real numbers with a &lt; b &lt; c &lt; d. We need to express a, b…

Q: Show that if a and b are real numbers and a!=0 then there is unique number r such that ar+b=0

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Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: E. On the right: a. r*ak + r*(-ak) = r*(ak + (-ak)) b. r*(ak + (-ak)) = r*0 c. r*0 = 0 F. So, r*(aj…

A: the last three lines also proves b and c too.

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: Show that this number is Irrational number

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Q: Prove that for all real numbers Ex)y= -(1u)

A: We have to prove that for all real numbers (- x)y= - (xy)

Q: For any integers a and b, a + b ≥ 15 implies that a ≥ 8 or b ≥ 8.

A: Let a+b≥15, where a,b are integers.   Case 1: b&lt;8 Then: b&lt;8⇒-b&gt;-8⇒15-b&gt;15-8⇒a≥15-b&gt;7…

Q: Consider the following theorem: There do not exist three consecutive odd integers a, b and c such…

A: In the last , I have written the theorem " There does not exist three consecutive odd integers…

Q: Let Z be the set of all integers and Q be the set of all rational numbers and R be the set of all…

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Q: 2. Let x be irrational real number. Prove that 2x+3 is irrational

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Q: Which choice gives an example that supports the conjecture, and a counterexample that nows the…

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