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Standard XII

Mathematics

Difference of Sets

If A = x:x is...

Question

If $A = {x : x is a multiple of 3}$ and $B = {x : x is a multiple of 5}$ , then $A - B$ is

$¯ A$ $\cap$ B

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A $\cap$ $¯ B$ .

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$¯ A$ $\cap$ $¯ B$ .

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$\frac{}{A \cap B}$

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Solution

The correct option is B
A $\cap$ $¯ B$ .

$A = {x : x is a multiple of 3}$

$\Rightarrow A = {3, 6, 9 \dots .}$

and $B = {x : x is a multiple of 5}$

$\Rightarrow B = {5, 10, 15 \dots .}$

Since $A - B = A - (A \cap B) = (A \cap ¯ B$ )

or we can say $A - B = {x : x is a multiple of 3 but not a multiple of 5}$

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If A={x:x is a multiple of 3 } and B={x:x is a multiple of 5 } , then A−B is

The correct option is B A ∩ ¯B . A={x:x is a multiple of 3} ⇒A={3,6,9….} and B={x:x is a multiple of 5} ⇒B={5,10,15….} Since A−B=A–(A∩B)=(A∩¯B) or we can say A–B={x:x is a multiple of 3 but not a multiple of 5}

If $A = {x : x is a multiple of 3}$ and $B = {x : x is a multiple of 5}$ , then $A - B$ is