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Equal Sets

State, whethe...

Question

State, whether the following pairs of sets are equal or not :
If they are equal then write $1$ , else write $0$ .
$A = 2, 4, 6, 8$ and $B =$ { $2 n : n ϵ N$ and $n < 5$ }

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Solution

$A = {2, 4, 6, 8}$
$B = {2 n : n \in N, n < 5}$
$n \in N$ and $n < 5$
$∴ n = 1, 2, 3, 4$
$∴ B = {2 (1), 2 (2), 2 (3), 2 (4)}$
$B = {2, 4, 6, 8}$
$∴$ Sets $A$ and $B$ are equal.

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

(i) A= ${2, 4, 6, 8}$ and $B = {2 n : n \in N a n d n < 5}$

(ii) $M = {x : x \in W a n d x + 3 < 8} a n d N = {y : y = 2 n - 1, n \in N a n d n < 5}$

(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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