GRO 5. Consider the infinite set of positive integers {1, 2, 3,..}. Find a way to name definite subsets as lines and other definite subsets as planes in such a manner that the incidence axioms will automatically hold as in the manner of the previous tetra- hedron model. (Hint: Let one line consist of the points 3, 4, 5,.. .) ing model in which there is fall
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Please answer question 5 (2.3)
![Which axiom is not satisfied?
3. Consider the following system of points, lines, and planes:
Points: S {1, 2, 3.4, 5}
Lines: (1, 2. 3}, {1.4). {1, 5}. {2, 4}. {2, 5}. {3, 4}, {3, 5}. {4. 5}
Planes: {1, 2, 3, 4}. {1, 2, 3, 5}, {1, 2, 3}. {1, 4, 5}. {2, 4, 5}, {3, 4, 5}
Which incidence axioms are satisfied here?
4. Consider the following system of points, lines, and planes:
{1, 2, 3, 4}
Lines: {1, 2, 4}. {1, 3}, {2, 3}, {3, 4}
Planes: {1, 2, 3}, {1, 3, 4}, {2, 3, 4}
Points: S =
ory
Which incidence axioms are satisfied in this model?
GROUP B
5. Consider the infinite set of positive integers {1, 2, 3, . . .}. Find a way to name
definite subsets as lines and other definite subsets as planes in such a manner that
the incidence axioms will automatically hold as in the manner of the previous tetra-
hedron model. (Hint: Let one line consist of the points 3, 4, 5, . . .)
6. The 7-Point Projective Plane Consider the following model, in which there is
only one plane, the universal set S itself.
line passing
through 2, 4, 7
{1, 2, 3, 4, 5, 6, 7}
{1, 2, 3}, l2 = {1, 4, 5}, lz = {3,7, 5}, €4 = {1, 6, 7},
ls = {2, 5, 6}, lo = {3, 4, 6}, l7 = {2, 4, 7}
{1, 2, 3, 4, 5, 6, 7}
Points: S
%3D
Lines: l1
%3D
%3D
4
6.
%3D
Plane: P
%3D
Which incidence axioms are satisfied? (Compare this model with the committee
structure in the Flying Aviators Club of Problem 11, Section 2.2.)
7. The Four-Point Affine Plane Show that the model depicted here for four points
satisfies the axioms for an affine plane, consisting of Axiom I-1, the pertinent part
of Axiom I-5 dealing with a single plane, and the Parallel Postulate (a unique line
exists that passes through a given point parallel to-does not intersect-a given line).
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