ani69
14.10.2019 •
Mathematics
8. (8 marks) prove that for all integers m and n, m + n and m-n are either both even or both odd
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Ответ:
Answer with explanation:
Let m and n are integers
To prove that m+n and m-n are either both even or both odd.
1. Let m and n are both even
We know that sum of even number is even and difference of even number is even.
Suppose m=4 and n=2
m+n=4+2=6 =Even number
m-n=4-2=2=Even number
Hence, we can say m+n and m-n are both even .
2. Let m and n are odd numbers .
We know that sum of odd numbers is even and difference of odd numbers is even.
Suppose m=7 and n=5
m+n=7+5=12=Even number
m-n=7-5=2=Even number
Hence, m+n and m-n are both even .
3. Let m is odd and n is even.
We know that sum of an odd number and an even number is odd and difference of an odd and an even number is an odd number.
Suppose m=7 , n=4
m+n=7+4=11=Odd number
m-n=7-4=3=Odd number
Hence, m+n and m-n are both odd numbers.
4.Let m is even number and n is odd number .
Suppose m=6, n=3
m+n=6+3=9=Odd number
m-n=6-3=3=Odd number
Hence, m+n and m-n are both odd numbers.
Therefore, we can say for all inetegers m and n , m+n and m-n are either both even or both odd.Hence proved.
Ответ:
Total length of the ribbon,
→ 12 feet
Total ribbon used by Holy,
→ 3.5 feet
Now we have to,
find the maximum length of ribbon, that holly can use to wrap the rest of her gift.
The formula we use,
→ Length of ribbon - Ribbon used by Holy
Let's find the required value,
→ 12 - 3.5 = 8.5 feet
Therefore, the length of ribbon holly can use to wrap the rest of her gift is 8.5 feet.