If A - x - x -3 n - n - Z and B - x - x -4 n - n - Z then find A - B

We have A=x:xϵ Zand x is a multiple of 3 B=x:xϵ Z and x is a multiple of 4 ∴ A∩ B=A=x:xϵ Z and x is a multiple of both 3 and 4 =x:xϵ Z and x is a multiple of 12 ...

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Byju's Answer

Standard XII

Mathematics

Theorems for Differentiability

If A = x : x ...

Question

If $A = {x : x = 3 n, n ϵ Z}$ and $B = {x : x = 4 n, n ϵ Z}$ then find $A \cap B$ .

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Solution

We have
A={ $x : x ϵ Z$ and x is a multiple of 3}

B={ $x : x ϵ Z$ and x is a multiple of 4}

$∴ A \cap B$ =A={ $x : x ϵ Z$ and x is a multiple of both 3 and 4}

={ $x : x ϵ Z$ and x is a multiple of 12}= ${x : x = 12 n, n ϵ Z}$

Hence, $A \cap B = {x : x = 12 n, n ϵ Z}$

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If A={x:x=3n,nϵZ} and B={x:x=4n,nϵZ} then find A∩B.

We have A={x:xϵZand x is a multiple of 3} B={x:xϵZ and x is a multiple of 4} ∴ A∩B=A={x:xϵZ and x is a multiple of both 3 and 4} ={x:xϵZ and x is a multiple of 12}={x:x=12n,nϵZ} Hence, A∩B={x:x=12n,nϵZ}

If $A = {x : x = 3 n, n ϵ Z}$ and $B = {x : x = 4 n, n ϵ Z}$ then find $A \cap B$ .

We have
A={ $x : x ϵ Z$ and x is a multiple of 3}

B={ $x : x ϵ Z$ and x is a multiple of 4}

$∴ A \cap B$ =A={ $x : x ϵ Z$ and x is a multiple of both 3 and 4}

={ $x : x ϵ Z$ and x is a multiple of 12}= ${x : x = 12 n, n ϵ Z}$

Hence, $A \cap B = {x : x = 12 n, n ϵ Z}$