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Equivalent Sets

If X=Natural ...

Question

If $X = {N a t u r a l n u m b e r s}$ and $Y = {P o s i t i v e i n t e g e r s}$ then write down the elements of $X & Y$ .State whether the sets $X & Y$ are equivalent.Are they equal?

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Solution

Determining the given sets are equivalent and equal or not
Given that $X = {N a t u r a l n u m b e r s}$ $\Rightarrow X = {1, 2, 3, 4, 5, . . . . .}$
And given that $Y = {P o s i t i v e i n t e g e r s}$ $\Rightarrow Y = {1, 2, 3, 4, 5, . . . . . .}$
From set $X & Y$ , both having same elements.
$∴ X = Y$
Since all equal sets are equivalent.
$∴ X & Y$ are equivalent and equal.

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