Let S = 4 , 6 , 9 and T = 9 , 10 , 11 , … , 1000 . If A = a 1 + a 2 + … + a k : k ∈ N , a 1 , a 2 , a 3 , … , a k ∈ S then the sum of all the elements in the set T - A is equal to _______.

Step-by-step solution

Given, S = 4 , 6 , 9   &   T = 9 , 10 , 11 … . . 1000 Also given A a 1 + a 2 + … . . + a k : K ∈ N   &   a i ∈ S Now here by the definition of set ' A ' A = a : a = 4 x + 6 y + 9 z Now checking number we will get from equation a = 4 x + 6 y + 9 z Put x = y = 0   &   z = 1 we get a = 9 Put x = y = 1   &   z = 0 we get a = 10 Put x = 0 ,   y = 2   &   z = 0 we get a = 12 Put x = 1 ,   y = 0   & &#1