hannahbrooke0304
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for which of the following conditions will the sum of integers m and n always be an odd number?

F. m is an odd integer
G. n is an odd integer
H. m and n are both odd integers
J. m and n are both even integers
K. m is an odd integer and n is an even integer​

Respuesta :

opudodennis

Answer:

Option K

m is an odd integer and n is an even integer​

Step-by-step explanation:

The sum of intergers when one is even and another is odd results into an even number. Take for example, if x is even and the next number x+1 their sum will be 2x+1. The presence of +1 at the end shows the number is not divisible by 2 hence an odd number.

Practically, if you add 2+3=5 and 2 is even number while 3 is odd, clearly the sum being 5 is an odd number.

Otherwise, if you add two even numbers or two odd numbers the sum will be an even number.

MrRoyal

Even numbers can be divided by 2 without leaving a remainder, while odd numbers can't.

The true condition is condition K: m is an odd integer and n is an even integer​

If m is odd and n is odd, then the sum will be even

This means that: Conditions F, G and H cannot be true

As an illustration, we have:

[tex]m + n= 5+ 7[/tex]

[tex]m + n= 12[/tex]

12 is even.

The result will always be even, provided that m and n are odd numbers.

If m is even and n is even, then the sum will be even

This means that: Conditions J cannot be true

As an illustration, we have:

[tex]m + n = 6 + 8[/tex]

[tex]m + n =14[/tex]

14 is even.

The result will always be even, provided that m and n are even numbers.

If m is odd and n is even, then the sum will be odd

This means that: Conditions K is true

As an illustration, we have:

[tex]m + n = 6 + 7[/tex]

[tex]m + n = 13[/tex]

13 is odd.

The result will always be odd, provided that m is odd while, n is even.

Hence: the true condition is:

K. m is an odd integer and n is an even integer​

Read more about odd and even integers at:

https://brainly.com/question/490943

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