Answer:
(Option B
(Option C
Step-by-step explanation:
Concept:
We will start by explaining each option one after the other
Step 1:
The sum of two odd numbers
Let the first odd number be
[tex]2a+1[/tex]
Let the second odd number be
[tex]2B+1[/tex]
By adding the two numbers, we will have
[tex]2a+1+2B+1=2(a+B)+2[/tex]
Hence,
The sum of two odd numbers is even
Step 2:
The difference of two odd number
Let the first odd number be
[tex]2a+1[/tex]
Let the second odd number be
[tex]2B+1[/tex]
To find their difference, we will have
[tex]2a+1-(2B+1)=2a+1-2B-1[/tex]
[tex]=2a-2B[/tex]
Hence,
The difference between two odd numbers is even
Step 3:
Let the first even number be
[tex]2a[/tex]
Let the second odd number be
[tex]2B+1[/tex]
By adding the two numbers, we will have
[tex]2a+2B+1[/tex]
Hence,
The sum of an odd number and an even number is odd
Step 4:
The difference between an odd number and an even number
Let the first even number be
[tex]2a[/tex]
Let the second odd number be
[tex]2B+1[/tex]
Hence,
The difference will be
[tex]2a-(2B+1)[/tex]
[tex]2a-2B-1[/tex]
Hence,
The difference between an odd number and an even number is odd
Therefore,
The correct answers are OPTION B and OPTION C
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