If U = x: x5 - 6x4 + 11x3 - 6x2 = 0 and A = x: x2 - 5x + 6 = 0 and B = x: x2 - 3x + 2 = 0 then (A ∩ B)' =

Question

If U = x: x5 - 6x4 + 11x3 - 6x2 = 0 and A = x: x2 - 5x + 6 = 0 and B = x: x2 - 3x + 2 = 0 then (A ∩ B)' = (A)  1,3  (B)  1,2,3  (C)  0,1,3  (D)  0,1,2,3

Tardigrade Admin · Accepted Answer

∵ U = x: x5-6x4+11x3-6x2 = 0 = 0, 1, 2, 3 A = x: x2 - 5x+6 = 0 = 2, 3 and B = x: x2-3x+2 = 0 = 1, 2 ∴ A ∩ B = 2 Hence, (A ∩ B)' = U - (A ∩ B) = 0, 1, 2, 3 - 2 = 0, 1, 3

Q. If $U = {x : x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0}$ and
$A = {x : x^{2} - 5 x + 6 = 0}$ and $B = {x : x^{2} - 3 x + 2 = 0}$ , then $(A \cap B)^{'} =$

${1, 3}$

${1, 2, 3}$

${0, 1, 3}$

${0, 1, 2, 3}$

$∵ U = {x : x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0} = {0, 1, 2, 3}$
$A = {x : x^{2} - 5 x + 6 = 0} = {2, 3}$
and $B = {x : x^{2} - 3 x + 2 = 0} = {1, 2}$
$∴ A \cap B = {2}$
Hence, $(A \cap B)^{'} = U - (A \cap B)$
$= {0, 1, 2, 3} - {2} = {0, 1, 3}$

Q. If U={x:x5−6x4+11x3−6x2=0} and A={x:x2−5x+6=0} and B={x:x2−3x+2=0}, then (A∩B)′=

{1,3}

{1,2,3}

{0,1,3}

{0,1,2,3}