Question

HELP PLEASE! The sets L,P and C are the sets of all the points on a given straight line, a given plane and a given circle respectively. Given that n(L intersection P)> 1 and n(C intersection P)<2, write down the possible values of n( L intersection C). If L1 is the set of all the points on a second straight line such that n(L1 intersection P)=1, write down the possible values of n(L1 intersection C).

Answer 1

@eigenschmeigen @experimentX

Answer 2

guess is 1 and 1 or 2 for next

Answer 3

ok, so the value of n(L intersection P) is number of points lying both on L and P, so it literally means the number of times L intersects P lol.

n(L intersection P) > 1 implies L lies in P ( L is a subset of P)

n(C intersection P) < 2 now implies

n(C intersection L) < 2 , since L is a subset of P

it also means that the circle either lies tangent to P or does not touch P at all

in the first case this means n(C intersection L) = 0

in the second case this means n(C intersection L) = 1 or n(C intersection L) = 0

sorry if i have misunderstood, i haven't done much with sets

Answer 4

Oh ... i didn't consider 0

Answer 5

n(C intersection L) = 0 looks like

Answer 6

n(C intersection L) = 1 looks like

Answer 7

if that makes sense

Answer 8

I think he same ... first case.

Answer 9

second case