The sets A - x - x - N and 13 - 2x - 1 andB - y - y - Z and -30 - y - - 25 are which type of sets-

Given A = {x : x ∈ nbsp;N and 13 gt; 2x + 1}. For x ∈ N, 13 nbsp;2x + 1 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp;nbsp;⇒ ...

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Standard IX

Mathematics

Sets

The sets A = ...

Question

The sets

$A = {x : x \in N and 13 > 2 x + 1}$ and

$B = {y : y \in Z and - 30 \leq y < - 25}$ are which type of sets?

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Solution

$Given A = {x : x \in N and 13 > 2 x + 1} .$

For $x \in N,$ $13 > 2 x + 1$
$\Rightarrow 12 > 2 x$
$\Rightarrow 6 > x$
i.e., $x < 6$

$∴ A = {1, 2, 3, 4, 5}$
$\Rightarrow n (A) = 5$ ( 1 mark )

$B = {y : y \in Z and - 30 \leq y < - 25}$
$\Rightarrow B = {- 30, - 29, - 28, - 27, - 26}$
$\Rightarrow n (B) = 5$ ( 1 mark )

As $n (A) = n (B),$ the sets A and B are equivalent, though they are not equal. ( 1 mark )

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The sets

$A = {x : x \in N and 13 > 2 x + 1}$ and

$B = {y : y \in Z and - 30 \leq y < - 25}$ are ___ sets.

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$A = {x : x ϵ N and 13 > 2 x + 1}$ and
$B = {y : y ϵ N a n d 1 \leq y < 6}$ are ________.

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The sets A={x:x∈N and 13>2x+1} and B={y:y∈Z and −30≤y<−25} are which type of sets?

Given A={x:x∈N and 13>2x+1}. For x∈N, 13>2x+1 ⇒12>2x ⇒6>x i.e., x<6 ∴A={1,2,3,4,5} ⇒n(A)=5 ( 1 mark ) B={y:y∈Z and −30≤y<−25} ⇒B={−30,−29,−28,−27,−26} ⇒n(B)=5 ( 1 mark ) As n(A)=n(B), the sets A and B are equivalent, though they are not equal. ( 1 mark )

The sets

$A = {x : x \in N and 13 > 2 x + 1}$ and

$B = {y : y \in Z and - 30 \leq y < - 25}$ are which type of sets?