Let S= 4,6,9 and T= 9,10,11, ldots, 1000 . If A = a 1+ a 2+ ldots+ a k: k ∈ N , a 1, a 2., .a3, ldots, ak ∈ S then the sum of all the elements in the set T - A is equal to

Question

Let S= 4,6,9 and T= 9,10,11, ldots, 1000 . If A = a 1+ a 2+ ldots+ a k: k ∈ N , a 1, a 2., .a3, ldots, ak ∈ S then the sum of all the elements in the set T - A is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

S = 4,6,9 T = 9,10,11 ldots .1000 A a 1+ a 2+ ldots . .+ a k: K ∈ N a i ∈ S Here by the definition of set 'A' A= a: a=4 x+6 y+9 z Except the element 11, every element of set T is of the form 4 x+6 y+9 z for some x , y , z ∈ W ∴ T - A = 11

Q. Let $S = {4, 6, 9}$ and $T = {9, 10, 11, \dots$ , 1000 . If $A = {a_{1} + a_{2} + \dots + a_{k} : k \in N, a_{1}, a_{2}$ , $a_{3}, \dots, a_{k} \in S}$ , then the sum of all the elements in the set $T - A$ is equal to

$S = {4, 6, 9} T = {9, 10, 11 \dots .1000}$
$A {a_{1} + a_{2} + \dots .. + a_{k} : K \in N} & a_{i} \in S$
Here by the definition of set 'A'
$A = {a : a = 4 x + 6 y + 9 z}$
Except the element 11, every element of set $T$ is of the form $4 x + 6 y + 9 z$ for some
$x, y, z \in W$
$∴ T - A = {11}$

Q. Let S={4,6,9} and T={9,10,11,…, 1000 . If A={a1​+a2​+…+ak​:k∈N,a1​,a2​, a3​,…,ak​∈S}, then the sum of all the elements in the set T−A is equal to

S={4,6,9}T={9,10,11….1000} A{a1​+a2​+…..+ak​:K∈N}&ai​∈S Here by the definition of set 'A' A={a:a=4x+6y+9z} Except the element 11, every element of set T is of the form 4x+6y+9z for some x,y,z∈W ∴T−A={11}

Q. Let $S = {4, 6, 9}$ and $T = {9, 10, 11, \dots$ , 1000 . If $A = {a_{1} + a_{2} + \dots + a_{k} : k \in N, a_{1}, a_{2}$ , $a_{3}, \dots, a_{k} \in S}$ , then the sum of all the elements in the set $T - A$ is equal to

$S = {4, 6, 9} T = {9, 10, 11 \dots .1000}$
$A {a_{1} + a_{2} + \dots .. + a_{k} : K \in N} & a_{i} \in S$
Here by the definition of set 'A'
$A = {a : a = 4 x + 6 y + 9 z}$
Except the element 11, every element of set $T$ is of the form $4 x + 6 y + 9 z$ for some
$x, y, z \in W$
$∴ T - A = {11}$