Answer:
The product of any even number and any integer is always even is proved
Solution:
Proof that any integer multiplied by 2 is even comes from the simple fact that every even number has 2 as a factor, the product of an even number with any even or odd number, will also have 2 as a factor, and thus also be even.
Any even number can be expressed as [tex]2^k[/tex] ,
where k>= 1 and let ‘a’ be any integer.
Then the result of any even number multiplied by any integer is
[tex]2^k \times a[/tex]
which is divisible by 2 yielding no remainder, and hence by definition an even number.
Hence any integer multiplied by an even number will always be an even number.
