Question

If $X=\{Naturalnumbers\}$ and $Y=\{Positiveintegers\}$ then write down the elements of $X\&Y$.State whether the sets $X\&Y$ are equivalent.Are they equal?

Answer 1

Determining the given sets are equivalent and equal or not

Given that $X=\{Naturalnumbers\}$$\Rightarrow X=\{1,2,3,4,5,.....\}$

And given that $Y=\{Positiveintegers\}$$\Rightarrow Y=\{1,2,3,4,5,......\}$

From set $X\&Y$, both having same elements.

$\therefore X=Y$

Since all equal sets are equivalent.

$\therefore X\&Y$are equivalent and equal.