Every positive integer is to be colored according to two rul

Every positive integer is to be colored according to two rules.

1. Each number is green or red

2. the sum of any two different numners of a given color is that same color.

in how many different ways can this be done.

a. 0                         b.2                  c.4                      d.6                   e.More than 6

Solution

CaseI : If the positive even numbers are colored green and positive odd numbers are colored red

Then, as sum of two odd numbers is an even number, so whenever we sum up any two numbers which are colored red, then we get a number which is colored green.

CaseII:

If the positive even numbers are colored red and positive odd numbers are colored green

Then, as sum of two odd numbers is an even number, so whenever we sum up any two numbers which are colored green, then we get a number which is colored red.

Thus,we infer that the given event is an impossible event.

Hence, the required probability is zero.

Consequently, the correct option is A.