If A- x-x-4k-1- k- and k-12 and B-x-x-5k- k- and k-6- then nA- B is

A= {x:x=4k+1, k∈𝕎 and k≤12} = {1,5,9,13,17,21,25,29,33,37,41,45,49} n(A)=13 B= {x:x=5^k, k∈𝕎 and k≤6 } = {1,5,5^2,5^3,5^4,5^5,5^6 } n(B)=7 A∩ B = nbsp; {1,5 ...

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Byju's Answer

Standard XII

Mathematics

Validation of Statement

If A= x:x=4k+...

Question

If $A = {x : x = 4 k + 1, k \in W and k \leq 12}$ and $B = {x : x = 5^{k}, k \in W and k \leq 6}$ , then $n (A Δ B)$ is

17

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Solution

The correct option is B $14$
$A = {x : x = 4 k + 1, k \in W and k \leq 12}$
$= {1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49}$
$n (A) = 13$

$B = {x : x = 5^{k}, k \in W and k \leq 6}$
$= {1, 5, 5^{2}, 5^{3}, 5^{4}, 5^{5}, 5^{6}}$
$n (B) = 7$

$A \cap B = {1, 5, 25}$
$\Rightarrow n (A \cap B) = 3$

$∴ n (A Δ B) = n (A \cup B) - n (A \cap B) = n (A) + n (B) - 2 n (A \cap B) = 13 + 7 - 6 = 14$

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If A={x:x=4k+1,k∈W and k≤12} and B={x:x=5k,k∈W and k≤6}, then n(AΔB) is

The correct option is B 14A={x:x=4k+1,k∈W and k≤12} ={1,5,9,13,17,21,25,29,33,37,41,45,49} n(A)=13 B={x:x=5k,k∈W and k≤6} ={1,5,52,53,54,55,56} n(B)=7 A∩B={1,5,25} ⇒n(A∩B)=3 ∴n(AΔB)=n(A∪B)−n(A∩B)=n(A)+n(B)−2n(A∩B)=13+7−6=14

If $A = {x : x = 4 k + 1, k \in W and k \leq 12}$ and $B = {x : x = 5^{k}, k \in W and k \leq 6}$ , then $n (A Δ B)$ is