exactly one
A.: Switzerland did become independent. B is false, because the Hapsburgs did defeat the Turkish siege of Vienna. C is false, because many members of the House of Hapsburg served as Holy Roman Emperors. D is false, because the Hapsburg rulers served not only as Kings of Austria, but also of Hungary. pmr_420 penfosster
They are collinear points that lie on the same line
# 1
Compass
Select one: a. False; the angles may be supplementary. b. True c. False; one angle may be in the interior of the other. d. False; the angles may be adjacent.
5 its 4
4*3/2 = 6 lines.
zero= false, non-zero=true
Yes. If all the question's parts are true, then the answer is true. If all the question's parts are false, then the answer is false. If one of the question's parts is false and the rest true, then the answer is false. Logically, this is illustrated below using: A = True, B = True, C = True, D = False, E = False, F = False A and B and C = True D and E and F = False A and B and D = False If you add NOT, it's a bit more complicated. A and NOT(D) = True and True = True NOT(D) and D = True and False = False NOT(A) and NOT(B) = False and False = False Using OR adds another layer of complexity. A OR NOT(E) = True OR True = True NOT(D) OR D = True OR False = False NOT(A) OR NOT(B) = False OR False = False Logic is easy once you understand the rules.
A. Coincident
In Euclidean Geometry, two non-coplanar lines are two lines in 3-dimensional space for which no single plane contains allpoints in both lines. For any two lines in three dimensional space, there is always at least one plane that contains all points in one line and at least one point in the other line. But there is not always (in fact it's quite rare) that any plane will contain all points in both lines. When it happens, there is only one such plane for any two distinct lines. Note that, any two lines in 3-dimensional space that intersect each other mustbe coplanar. Also, any two lines in 3-dimensional space that are parallel to each other must also be coplanar. So, in order to be non-coplanar, two lines in 3-dimensional space must a) not intersect each other at any point, and b) not be parallel to each other. (As it turns out, this dual condition is not only necessary, but sufficient for non-coplanarity.) Also note that, as a test for coplanarity of two lines, you need only test two points on each line, for a total of four points, because all points on a single line are, by definition, on the same plane. In fact, all you really have to do is test a single point on one line against three other points (one on the same line and two on the other line), because, by definition, any three points in 3-dimensional space are on the same plane. For example, consider any two distinct points on line m (A and B), and any two distinct points on line l (C and D). Points A and B are obviously coplanar because they are colinear (in fact, they are coplanar in the infinite number of planes that contain this line). Point C on line l is also coplanar with points A and B, because by definition, any 3 non-colinear points in 3-dimensional space define a plane (however, if point C is not on line m, the number of planes that contain all three points is immediately reduced from infinity to one). So the coplanarity test for the first three points is trivial - they are coplanar no matter what. However, it is not at all certain that point D will be on the same plane as points A, B, and C. In fact, for any two random lines in 3-dimensional space, the probability that the four points (two on each line) are coplanar is inifinitesimally small. But, if the fourth point, the one not used to define the plane, is nevertheless coplanar with the three points that define the plane, then lines l and m are coplanar. Note that, though I specified that points A and B on line m must be distinct, and that points C and D on line l must be distinct, I did not specify that C and D must both be distinct from both A and B. That is because, if, for example, A and C are the same (not distinct) point, then, obviously, lines m and l intersect, at point A, which is the same as point C. If this is the case, then the question of whether D is on the same plane as A, B, and C is trivial, because you really only have 3 distinct points, and any three distinct points alwaysshare a plane. That is why intersecting lines (lines that share a single point) are always coplanar. But you're asking about non-coplanar lines. So, basically, if any point on either of the two lines is not coplanar with the other three points (one on the same line and two on the other line), then the lines are non-coplanar.
coplanar
Yes.
zero= false, non-zero=true
True AND False OR True evaluates to True. IT seems like it does not matter which is evaluated first as: (True AND False) OR True = False OR True = True True AND (False OR True) = True AND True = True But, it does matter as with False AND False OR True: (False AND False) OR True = False OR True = True False AND (False OR True) = False AND True = False and True OR False AND False: (True OR False) AND False = True AND False = False True OR (False AND False) = True OR False = True Evaluated left to right gives a different answer if the operators are reversed (as can be seen above), so AND and OR need an order of evaluation. AND can be replaced by multiply, OR by add, and BODMAS says multiply is evaluated before add; thus AND should be evaluated before OR - the C programming language follows this convention. This makes the original question: True AND False OR True = (True AND False) OR True = False OR True = True
The answer depends on where the points A, B, C and X are. And since you have not bothered to provide that information, I cannot provide a sensible answer.