What is the area of a triangle with a base of 74 and a height of 17
1 answer:
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Answer:
Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))
1. R is reflexive if for each element a∈B, aRa.
2. R is symmetric if satisfies that if aRb then bRa.
3. R is transitive if satisfies that if aRb and bRc then aRc.
Then, our set B is .
a) We need to find a relation R reflexive and transitive that contain the relation
Then, we need:
1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,
2. Observe that
- 1R4 and 4R1, then 1 must be related with itself.
- 4R1 and 1R4, then 4 must be related with itself.
- 4R1 and 1R2, then 4 must be related with 2.
Therefore is the smallest relation containing the relation R1.
b) We need a new relation symmetric and transitive, then
- since 1R2, then 2 must be related with 1.
- since 1R4, 4 must be related with 1.
and the analysis for be transitive is the same that we did in a).
Observe that
- 1R2 and 2R1, then 1 must be related with itself.
- 4R1 and 1R4, then 4 must be related with itself.
- 2R1 and 1R4, then 2 must be related with 4.
- 4R1 and 1R2, then 4 must be related with 2.
- 2R4 and 4R2, then 2 must be related with itself
Therefore, the smallest relation containing R1 that is symmetric and transitive is
c) We need a new relation reflexive, symmetric and transitive containing R1.
For be reflexive
- 1 must be related with 1,
- 2 must be related with 2,
- 3 must be related with 3,
- 4 must be related with 4
For be symmetric
- since 1R2, 2 must be related with 1,
- since 1R4, 4 must be related with 1.
For be transitive
- Since 4R1 and 1R2, 4 must be related with 2,
- since 2R1 and 1R4, 2 must be related with 4.
Then, the smallest relation reflexive, symmetric and transitive containing R1 is
A line segment is a part of a line bound by two points; a ray is a line with one endpoint that extends to infinity in one direction. is the difference between a ray and line segment.
Option: C.
<u>Step-by-step explanation:</u>
A line is a set of multiple points that extends from one point to its opposite direction without any end. Ray and Line segments are the two parts that can occur in a line.
A ray is a line with an endpoint in which the line can be extended from that point to infinity in a direction. A line segment also another part line and it consists of two points. Moreover, The line is bounded between those points.
