Question

Show that any positive even integer is of the form 6q, or 6q + 2 or 6q + 4, where q is a positive integer.

Answer 1

Given :  even integer

To find : Show that any positive even integer is of the form 6q, or 6q + 2 or 6q + 4,

Solution:

a = bq + r

where 0 ≤ r < b

Hence without loosing generality any number can be represented as

6q , 6q + 1, 6q + 2 , 6q + 3 , 6q + 4 , 6q + 5    

6q = 2 ( 3q)   = 2k   hence even number

6q + 1 = 2(3q) + 1 = 2k + 1   hence odd number

6q + 2= 2 ( 3q+1)   = 2k   hence even number

6q + 3 = 2(3q+1) + 1 = 2k + 1   hence odd number

6q+ 4  = 2 ( 3q +2)   = 2k   hence even number

6q + 5 = 2(3q+2) + 1 = 2k + 1   hence odd number

6q   , 6q + 2 , 6q + 4   represent even integers

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Answer 2

Answer:

here is ur ans, plzz check it