Prove that the sum of two rational numbers is rational

Q: Find two irrational numbers a and b such that a is rational.

A:

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

A:

Q: How did early mathematicians discover that irrational numbers exist?

A:

Q: se a dire tional.

A: Introduction: A direct proof is a logical series of statements that demonstrate the truth or falsity…

Q: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

A:

Q: Prove that there is no rational number whose square is 12.

A:

Q: Is this statement true or false? Prove each true statement directly from the definitions and give a…

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

Q: at a, b and c be real numbers such that a #0 and ac+bc+c 4ac.

A: Given data is : a , b and c are real number such that a≠0 and ac+bc+c2<0 Show that b2>4ac

Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

A:

Q: 4. Show that Archimedean Principle is a consequence of the assertions that every interval (a, b)…

A:

Q: If a and b are both rational numbers such that a = 0 and b = 0, then is also a rational number.

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

Q: Prove that the product of two odd numbers is odd.

A: We first define a general odd number. Lets say that n is an integer. When we multiply any number by…

Q: Show that this number is Irrational number

A:

Q: Prove that the difference between the square of any odd integer and the integer itself is always an…

A: An odd integer is of the form 2n+1; n ∊ ℤ. Consider the difference between the square of an odd…

Q: Prove or disprove that there is a rational number x and an irrational number that xy is irrational.…

A: The given statement is false.

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

A:

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

A:

Q: Prove that 3+√3 is irrational.

A: As per guidelines we are supposed to solve the maximum one questions at  a time kindly post another…

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

A:

Q: Prove "A real number is said to be algebraic if is the root of a polynomial with integer…

A: Prove "A real number is said to be algebraic if is the root of a polynomial with integer…

Q: Express all real numbers greater than 6 and less than or equal to 7 in interval notation.

A:

Q: Consider the statement: "The sum of any two rational numbers is a rational number." Is it true or…

A: A rational number is a number that can be expressed as a fraction with integer values in the…