Prove that there exists no rational number x such that x2 = p, where p is a prime number (A prime number is a natural number (greater than 1) that cannot be written as a product of two smaller natural numbers.).

Q: Prove that if a and b are integers with a 0 and where + b - a = 0, x is a positive integer such that…

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Q: Prove by Contradiction that √6 + √8<√2

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Q: Let a,b and x be real numbers with a0. Show that there exists a rational number t such that a <

A: We know that the real numbers are densely ordered. This means that between any two distinct real…

Q: Prove that there does does not exist a unique positive real number, x, with the property that x…

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Q: Prove or disprove that there exist rational numbers x, y EQ such that √11: = x+y√5.

A: Prove or disprove that there exist rational numbers x, y  in Q such that √11 = x+y√5.

Q: Prove that the product of two integers, one of the form 3k₁ +2 and the other of the form 3k2 +2,…

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Q: Prove that if x and y are rational numbers such that x &gt; y, then there exists a rational number z…

A: We have to prove that If x and y are rational numbers such that x &gt; y Then there exists a…

Q: (7) The difference of two odd integers x and y is 4. Prove that x and y are relatively prime.

A: Given difference of two odd integers is 4.

Q: Prove that for any two integers a and b with b>0, there exist unique integers q (the quotient) and r…

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Q: Which proof method is used in above proof. O Proof by counterexample O Direct proof O Proof by…

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Q: Let A denote the set of positive rational numbers whose square is less than 2: A = {q ∈ Q : q > 0…

A: Given that  be the set of positive rational numbers whose square is less than . That is:.We need to…

Q: prove that for all positive integers therre exists two rational numbers such that there product is…

A: Let us consider two positive integers say 1 and 2. Now we find two rational numbers between them :…

Q: If a and b are positive integers such that gcd(a,b)=13, then find the sum of all possible distinct…

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Q: (i) Show that √6 + √7 is an algebraic number.

A: We are answering only the first question as per the guidelines. Please repost the other question to…

Q: prove that √2+√5 is not a rational number

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Q: Is every infinite subset of Z x (Z-{0}) a rational number?

A: Given: Infinite subset of ℤ×ℤ-0 To Prove: Every subset is a rational number. Rational Number: Any…

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: 1) Show that for all positive integers x, x! + 1 has a prime divisor greater than x.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Prove that for every positive integer n the number (1 – /2)" is not ratioanal.

A: Given: The given number is, (1-2)n where n is the positive integer.   To prove: The number (1-2)n is…

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.