Part 2. Each relation given below is a partial order. Draw the Hasse diagram for the partial order.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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![**Part 2**: Each relation given below is a partial order. Draw the Hasse diagram for the partial order.
(a) The domain is \(\{3, 5, 6, 7, 10, 14, 20, 30, 60\}\). The relation is defined as \(x \leq y\) if \(x\) evenly divides \(y\).
(b) The domain is \(\{a, b, c, d, e, f\}\). The relation is the set:
\[
\{(b, e), (b, d), (c, a), (e, f), (a, f), (a, a), (b, b), (c, c), (d, d), (e, e), (f, f)\}
\]
**Explanation of Hasse Diagrams:**
A Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, with elements ordered with respect to a transitive and antisymmetric reflexive binary relation.
1. **Elements in Diagrams**: Each element of the set is represented by a vertex in the diagram.
2. **Edges Without Direction**: If an element \(x\) is less than \(y\) (i.e., \(x \leq y\)) but there is no \(z\) such that \(x \leq z\) and \(z \leq y\), then \(x\) and \(y\) are connected by an edge, with \(x\) being lower than \(y\) in the drawing.
3. **No Redundant Edges**: There are no edges that can be inferred from transitivity.
4. **Visual Clarity**: Elements are often arranged such that all edges point upwards while minimizing crossing edges where possible to allow for easy reading of the diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27f445ea-1d9a-48bd-a007-85d03e874c3c%2Fc955e1b3-4d4a-4353-81b9-b49fcc74bc50%2Fs1u8c3_processed.png&w=3840&q=75)
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