If a and b are two natural numbers and if (a+b) is even,prove that (a-b) is also even
Answers
Answered by
10
If (a+b) is even then either both a and b will be even or both will be odd at the same time because the sum of an even number and an odd number is always odd.
We know that the difference of two even numbers or two odd numbers is always even so, b-a or a-b would also be even.
We know that the difference of two even numbers or two odd numbers is always even so, b-a or a-b would also be even.
tauseefwatto0:
These are the basics of Mathematics.
but th
There are such things that are technical. Those things are logical and need no proof.
but this question related to rational and irrational
nice point. I thought that it was related to the positive natural numbers.
but the answer would be in natural numbers
and they won't be irrational.
point to noted is that if a and b are rational then if a+b is even, a-b may not be even.
check it for a=4/3 and b=2/3.These are supposed values which tells us that rational numbers can not fulfill this condition.
And on the other hand, irrational numbers do not contain the even or odd numbers. Rational numbers contain both even and odd because it is their superset.
Answered by
7
Answer:
1st alternative:
Let us assume a,b as two even numbers 4 and 2
a = 4,b = 2
Then,
a+b=>4+2=6
a-b=>4-2=2
Here the results are even
OR
2nd alternative :
Let's assume a,b as two odd numbers
3 and 1
a = 3,b = 1
Then,
a+b=>3+1=4
a-b=>3-1=2
Here too the results are even
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