NICAL ENGINEERING

NICAL ENGINEERING PROGRAM, BSC$.$

$1.$ Let p$($x$)$ q$($x$)$ and r$($x$)$ be the following open statements:

p$($x$)$: x $^2-7$x $+10=0$

q$($x$)/($x $^2)-2$x $-3=0$

r$($x$)/$ x $<0$

Determine the truth or falsity of the following statements, where the universe is all integers. If a statement is either true or false, provide an explanation or counter example: $(6$ points$)$

a$.$ forall x$[$ p$($x$)$ neg r$($x$)]$

b$.$ exists x$[$q$($x$)->$ r$($x$)]$

c$.$ forall x$[$q$($x$)->$ r$($x$)]$

d$.$ exists x$[$p$($x$)->$ tau$($x$)]$