Let Z be the set of integers, if A={x∈Z:|x−3|(x2−5x+6)=1} and B={x∈Z:10<3x+1<22} , then the number of subsets of the set A×B is

For A, |x−3|=1⇒x=2,4 or x2−5x+6=0⇒x=2,3 but x≠3∴A={2,4}For B,B={4,5,6}n(A×B)=6 number of subsets =26

Let Z be the set of integers, if A={x∈Z:|x−3|(x2−5x+6)=1} and B={x∈Z:10<3x+1<22} , then the number of subsets of the set A×B is

For A, |x−3|=1⇒x=2,4 or x2−5x+6=0⇒x=2,3 but x≠3∴A={2,4}For B,B={4,5,6}n(A×B)=6 number of subsets =26

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Let Z be the set of integers, if $A = {x \in Z : {| x - 3 |}^{(x^{2} - 5 x + 6)} = 1}$ and $B = {x \in Z : 10 < 3 x + 1 < 22}$ , then the number of subsets of the set $A \times B$ is

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$2^{6}$

$2^{15}$

$2^{8}$

$2^{9}$

answer is A.

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For A, $| x - 3 | = 1 \Rightarrow x = 2, 4 o r x^{2} - 5 x + 6 = 0 \Rightarrow x = 2, 3 b u t x \neq 3$
$∴ A = {2, 4}$
For B,
$B = {4, 5, 6}$
$n (A \times B) = 6$
number of subsets $= 2^{6}$

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Let Z be the set of integers, if A={x∈Z:|x−3|(x2−5x+6)=1} and B={x∈Z:10<3x+1<22} , then the number of subsets of the set A×B is

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Let Z be the set of integers, if $A = {x \in Z : {| x - 3 |}^{(x^{2} - 5 x + 6)} = 1}$ and $B = {x \in Z : 10 < 3 x + 1 < 22}$ , then the number of subsets of the set $A \times B$ is