rsinchevici235 rsinchevici235
  • 02-10-2019
  • Mathematics
contestada


Give a direct proof for each of the following statements about the integers.

If x is even and y is odd, then x + y is odd.

Respuesta :

lyndalau86
lyndalau86 lyndalau86
  • 05-10-2019

Answer:

See explanation below

Step-by-step explanation:

If x is even, then we know that x = 2k for a k ≥1

If y is odd, then we know that y = 2j -1 for a j≥1

Therefore, x + y can be written similarly as:

[tex]x+y[/tex]

[tex]2k +(2j-1)\\2(k+j)-1[/tex]

And clearly, 2(k + j) -1 is odd.

Therefore, the sum x + y is an odd number.

Answer Link

Otras preguntas

-3 (y - 5) = 24 help?
The creation of an independent Israel was the goal of
Wildfires are frequent In the Great Basin shrub steppe. Every time there is a fire outbreak, much of the natural vegetation is destroyed. What is the MOST LIKEL
mr. murphy has a old coin that has 10 side.if a shape is a polygon,how many angle do it have
Rhubarb is used in making pies, tarts, and sauces. If a cook makes 2 pints of rhubarb sauce, will there be at least 5 cups of sauce made?
Ammonium hydroxide ionizes as follows: NH4OH(s) NH4 +(aq) + OH-(aq). If an excess of ammonium salt, such as NH4Cl (which ionizes to give NH4 +(aq) ions) is ad
What could the number -18 represent? Using the same situation, what would its opposite represent? What would 0 represent
Percent value greater than 1/5 and less than 1/2
what group consists entirely of organic molecules?
Where are proteins made