Let X = { n N : 1 n 50 } . If A = { n X : n is a multiple of 2 } and B = { n X : n is a multiple of 7 } , then the number of elements in the smallest subset of X containing both A and B is

Question

Let $X = {n \in N : 1 \leq n \leq 50}$ . If $A = {n \in X : n$ is a multiple of 2 $}$ and $B = {n \in X : n$ is a multiple of 7 $}$ , then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is ________.

Smart Achievers · Accepted Answer

(29)

Given, $A = {n \in X : n is a multiple of 2} = {2, 4, 6, \dots, 50}$

$B = {n \in X : n is a multiple of 7} = {7, 14, 21, 28, 35, 42, 49}$

Smallest subset of $X$ containing both $A$ and $B$ will be $A \cup B$ .

$∴$ $n (A \cup B) = n (A) + n (B) - n (A \cap B) = 25 + 7 - 3 = 29$

Solution

Q.
Let $X = {n \in N : 1 \leq n \leq 50}$ . If $A = {n \in X : n$ is a multiple of 2 $}$ and $B = {n \in X : n$ is a multiple of 7 $}$ , then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is ________.

Ans.
(29)

Given, $A = {n \in X : n is a multiple of 2} = {2, 4, 6, \dots, 50}$

$B = {n \in X : n is a multiple of 7} = {7, 14, 21, 28, 35, 42, 49}$

Smallest subset of $X$ containing both $A$ and $B$ will be $A \cup B$ .

$∴$ $n (A \cup B) = n (A) + n (B) - n (A \cap B) = 25 + 7 - 3 = 29$

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Solution

Q. Let X={n∈N:1≤n≤50}. If A={n∈X:n is a multiple of 2} and B={n∈X:n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.

Ans. (29) Given, A={n∈X:n is a multiple of 2}={2,4,6,…,50} B={n∈X:n is a multiple of 7}={7,14,21,28,35,42,49} Smallest subset of X containing both A and B will be A∪B. ∴ n(A∪B)=n(A)+n(B)-n(A∩B)=25+7-3=29

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Q.
Let $X = {n \in N : 1 \leq n \leq 50}$ . If $A = {n \in X : n$ is a multiple of 2 $}$ and $B = {n \in X : n$ is a multiple of 7 $}$ , then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is ________.

Ans.
(29)

Given, $A = {n \in X : n is a multiple of 2} = {2, 4, 6, \dots, 50}$

$B = {n \in X : n is a multiple of 7} = {7, 14, 21, 28, 35, 42, 49}$

Smallest subset of $X$ containing both $A$ and $B$ will be $A \cup B$ .

$∴$ $n (A \cup B) = n (A) + n (B) - n (A \cap B) = 25 + 7 - 3 = 29$