Question

translate the statement "The product of any two positive integers is always positive"into logical expression(using Nested Quantifiers)

Answer 1

Given that for all positive integers $x$ and $y$ ; $xy>0$

Now using Nested Quantifiers the above statement can be written into logical expression in two ways:

Either,

$\forall x\in Z$ , $\forall y\in Z$ : $((x>0)\land (y>0))\to (xy>0)$

Here $Z$ denote set of all integers.

Or,

$\forall x\in Z^+,$ $\forall y \in Z^+$ : $(xy>0)$

Here $Z^+$ denote set of all positive integers.