What is the negation of each of the following statement?

Question

1. Points R,S and T are collinear and T is not a point on the centered at R with radius RS Negation: Points R,S and T are not collinear and T is a point on the center at R with radius RS

is this correct?

1. Given a line l and a point P that is not on l, there is exactly one line through P that is parallel to l Negation: Given a line l and a point p that is on l, the is at least one line through P that is not parallel to l

is this correct? Thank you

Answer 1

Re (1), NO. The negation of a proposition of the form $A$ and $B$ is either not-$A$ or not-$B$ (and not not-$A$ and not-$B$).

Re (2), NO. For a start the negation of there is exactly one F is there are either no F's or more than one F.

There are interesting issues lurking in the background in the second case about how to construe the Given ... construction, but we can probably ignore them here.

Answer 2

Not correct, to negative and statement negate both sides and use or instead of maintaining and.

($A$ and $B)^{n}$ = ($A^{n}$ or $B^{n}$)

($A$ or $B)^{n}$ = ($A^{n}$ and $B^{n}$)