Question

Если m и k натуральные числа и m + k = 2m + 4,то какие из следуйщих утверждений верны:1) m - четное2)k - четное3) k - m - четное4)если m четное,то и k четное?Сделайте пожалуйста,с объяснением,а не так "ДА,Верно.НЕТ,не верно"

Answer 1

1) 4 верно, так как если m-четное, то и к-четное
Например м-2, то к-4
2+4=2*2+2
Например если не четное , то м-3 к-7
3+7=3*2+4

Answer 2

Problem Analysis

We are given that `m` and `k` are natural numbers and `m + k = 2m + 4`. We need to determine which of the following statements are true: 1) `m` is even. 2) `k` is even. 3) `k - m` is even. 4) If `m` is even, then `k` is even.

Let's analyze each statement one by one.

Statement 1: `m` is even

To determine if `m` is even, we can rearrange the given equation `m + k = 2m + 4` to isolate `m` on one side: ``` m = k - 4 ``` From this equation, we can see that `m` is expressed as the difference between `k` and a constant value of 4. Since `k` is a natural number, `m` will also be a natural number. However, we cannot determine if `m` is even or odd based on this equation alone.

Statement 2: `k` is even

Similarly, to determine if `k` is even, we can rearrange the given equation `m + k = 2m + 4` to isolate `k` on one side: ``` k = 2m + 4 - m k = m + 4 ``` From this equation, we can see that `k` is expressed as the sum of `m` and a constant value of 4. Since `m` is a natural number, `k` will also be a natural number. However, we cannot determine if `k` is even or odd based on this equation alone.

Statement 3: `k - m` is even

To determine if `k - m` is even, we can substitute the expression for `k` from the previous equation into the given equation `m + k = 2m + 4`: ``` m + (m + 4) = 2m + 4 2m + 4 = 2m + 4 ``` From this equation, we can see that `k - m` simplifies to 4. Since 4 is an even number, we can conclude that `k - m` is indeed even.

Statement 4: If `m` is even, then `k` is even

To determine if this statement is true, we need to consider the equation `m + k = 2m + 4`. If `m` is even, we can express it as `m = 2x` for some natural number `x`. Substituting this into the equation, we get: ``` 2x + k = 4x + 4 k = 2x + 4 ``` From this equation, we can see that `k` is expressed as the sum of `2x` and a constant value of 4. Since `2x` is always even (as it is a multiple of 2), `k` will also be even. Therefore, statement 4 is true.

Summary of Results

Based on our analysis, we can conclude the following: 1) Statement 1: We cannot determine if `m` is even or odd based on the given equation alone. 2) Statement 2: We cannot determine if `k` is even or odd based on the given equation alone. 3) Statement 3: `k - m` is even. 4) Statement 4: If `m` is even, then `k` is even.

Therefore, statements 3 and 4 are the only ones that are true.

Note: It is important to note that the analysis provided is based on the given equation and mathematical reasoning. If there are any additional constraints or information provided, it may alter the conclusions.