State- whether the following pairs of sets are equivalent or not-i A-x-x- N and 11- 2x -1 and B-y-y in W and 3- y - 9

Step 1: Find number of elements in set A Given A x:x∈ N and 11≥ 2x 1 As, 11≥2x 1, x∈ N ⇒ 11+1≥ 2x, x∈ N ⇒≥ 2x, x∈ N ⇒12/2x, x∈ N ⇒ 6≥ x and x∈ N ⇒ x ...

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Standard XII

Mathematics

Finite and Infinite Set

State, whethe...

Question

State, whether the following pairs of sets are equivalent or not:

i A= ${x : x \in N a n d 11 \geq 2 x - 1} a n d B = {y : y i n W a n d 3 \leq y \leq 9}$

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Solution

Step 1: Find number of elements in set A
Given A { $x : x \in N a n d 11 \geq 2 x - 1$ }

As, $11 \geq 2 x - 1, x \in N$

$\Rightarrow 11 + 1 \geq 2 x, x \in N$

$\Rightarrow\geq 2 x, x \in N$

$\Rightarrow \frac{12}{2} x, x \in N$

$\Rightarrow 6 \geq x a n d x \in N$

$\Rightarrow x = {1, 2, 3, 4, 5, 6}$

so, number of elements in $A = 6$

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Similar questions

State, whether the following pairs of sets are equal or not:

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(iii) $E = {x : x^{2} + 8 x - 9 = 0} a n d F = {1, - 9}$

(iv) $A = {x : x \in, x < 3} a n d B = {y : y^{2} - 3 y + 2 = 0}$ Two sets are equal, if both the sets have same (identical) elements.

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Finite and Infinite Set

Standard XII Mathematics

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State, whether the following pairs of sets are equivalent or not: i A={x:x∈N and 11≥2x−1} and B={y:y in W and 3≤y≤9}

Step 1: Find number of elements in set A Given A {x:x∈N and 11≥2x−1} As, 11≥2x−1,x∈N ⇒11+1≥2x,x∈N ⇒≥2x,x∈N ⇒122x,x∈N ⇒6≥x and x∈N ⇒x={1,2,3,4,5,6} so, number of elements in A=6

State, whether the following pairs of sets are equivalent or not:

i A= ${x : x \in N a n d 11 \geq 2 x - 1} a n d B = {y : y i n W a n d 3 \leq y \leq 9}$