Let A - x - x 2-9 - 0- x - Z and B - x - x -2-3- x - Z - Then the number of elements in A - B isA- 3B- 4C- 5D- 6

The correct option is B 4A= { 3, 2, 1,0,1,2,3} B= {0,1,2,3,4} n(A)=7 ,n(B)=5, nbsp; n( A∩ B)=4 n( A Δ B) = nbsp; n(A B) + n(B A) = n(A) n( A∩ B) + n(B) ...

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Standard XII

Mathematics

Difference of Two Sets

Let A = x : x...

Question

Let $A = {x : x^{2} - 9 \leq 0, x \in Z}$ and $B = {x : | x - 2 | < 3, x \in Z} .$ Then the number of elements in $A Δ B$ is

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Solution

The correct option is B $4$
$A = {- 3, - 2, - 1, 0, 1, 2, 3}$
$B = {0, 1, 2, 3, 4}$

$n (A) = 7, n (B) = 5, n (A \cap B) = 4$
$n (A Δ B) = n (A - B) + n (B - A)$
$= n (A) - n (A \cap B) + n (B) - n (A \cap B)$
$= 7 - 4 + 5 - 4$
$= 12 - 8$
$= 4$

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Let A={x:x2−9≤0,x∈Z} and B={x:|x−2|<3,x∈Z}. Then the number of elements in AΔB is

The correct option is B 4A={−3,−2,−1,0,1,2,3} B={0,1,2,3,4} n(A)=7,n(B)=5,n(A∩B)=4 n(AΔB)=n(A−B)+n(B−A) =n(A)−n(A∩B)+n(B)−n(A∩B) =7−4+5−4 =12−8 =4

Let $A = {x : x^{2} - 9 \leq 0, x \in Z}$ and $B = {x : | x - 2 | < 3, x \in Z} .$ Then the number of elements in $A Δ B$ is

The correct option is B $4$
$A = {- 3, - 2, - 1, 0, 1, 2, 3}$
$B = {0, 1, 2, 3, 4}$

$n (A) = 7, n (B) = 5, n (A \cap B) = 4$
$n (A Δ B) = n (A - B) + n (B - A)$
$= n (A) - n (A \cap B) + n (B) - n (A \cap B)$
$= 7 - 4 + 5 - 4$
$= 12 - 8$
$= 4$