If A -0-1-2-3-5- - -0-1-2-3- C -0-1-4-5- then n A - B - n B - C - n C - A is equal toA- 10B- 7C- 8D- 9

The correct option is C 8A B={5} ,B A={ } ⇒ AΔ B={5} B C={2,3} ,C B={4,5 } ⇒ BΔ C={2,3,4,5} C A={4} ,A C={2,3 } ⇒ CΔ A={2,3,4} ∴ n(AΔ B)++n(BΔ C)+n(CΔ A) =1 ...

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Standard XII

Mathematics

Difference of Two Sets

If A =0,1,2,3...

Question

If $A = {0, 1, 2, 3, 5}, B = {0, 1, 2, 3}, C = {0, 1, 4, 5}$ , then $n (A Δ B) + n (B Δ C) + n (C Δ A)$ is equal to

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Solution

The correct option is C $8$
$A - B = {5}, B - A = {}$
$\Rightarrow A Δ B = {5}$

$B - C = {2, 3}, C - B = {4, 5}$
$\Rightarrow B Δ C = {2, 3, 4, 5}$

$C - A = {4}, A - C = {2, 3}$
$\Rightarrow C Δ A = {2, 3, 4}$

$∴ n (A Δ B) + + n (B Δ C) + n (C Δ A)$
$= 1 + 4 + 3 = 8$

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If A={0,1,2,3,5},B={0,1,2,3},C={0,1,4,5}, then n(AΔB)+n(BΔC)+n(CΔA) is equal to

The correct option is C 8A−B={5},B−A={ } ⇒AΔB={5} B−C={2,3},C−B={4,5} ⇒BΔC={2,3,4,5} C−A={4},A−C={2,3} ⇒CΔA={2,3,4} ∴n(AΔB)++n(BΔC)+n(CΔA) =1+4+3=8

If $A = {0, 1, 2, 3, 5}, B = {0, 1, 2, 3}, C = {0, 1, 4, 5}$ , then $n (A Δ B) + n (B Δ C) + n (C Δ A)$ is equal to

The correct option is C $8$
$A - B = {5}, B - A = {}$
$\Rightarrow A Δ B = {5}$

$B - C = {2, 3}, C - B = {4, 5}$
$\Rightarrow B Δ C = {2, 3, 4, 5}$

$C - A = {4}, A - C = {2, 3}$
$\Rightarrow C Δ A = {2, 3, 4}$

$∴ n (A Δ B) + + n (B Δ C) + n (C Δ A)$
$= 1 + 4 + 3 = 8$