Question

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (e) If x is an even integer and y is an odd integer, then x^2 + y^2 is odd. Prove each of the following statements using a direct proof. (c) If x and y are rational numbers, then 3x + 2y is also a rational number. (d) If x and y are rational numbers, then 3x^2 + 2y is also a rational number.

          Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer.

Prove each of the following statements using a direct proof.
(e) If x is an even integer and y is an odd integer, then x^2 + y^2 is odd.

Prove each of the following statements using a direct proof.
(c) If x and y are rational numbers, then 3x + 2y is also a rational number.
(d) If x and y are rational numbers, then 3x^2 + 2y is also a rational number.

Added by Gonzalo F.

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