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jaychay
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Is the statement that I have circle is true ?
Because I feel like the solution in my textbook is wrong, I only learn that empty set is a subset of every set but it is not an element of a set.
Set Problems: Is My Statement about Circles True?
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In summary, circles are not considered polygons because they have a curved boundary instead of straight sides. A circle can only have one center, which is the point equidistant from all points on its boundary. It is possible for a circle to have a perimeter, which is equal to its circumference. Not all circles are congruent, as two circles must have the same radius to be congruent. Finally, a circle does not have sides and therefore cannot have an infinite number of sides.
Is the statement that I have circle is true ?
Because I feel like the solution in my textbook is wrong, I only learn that empty set is a subset of every set but it is not an element of a set.
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Evgeny.Makarov
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You are right: $\emptyset$ is not an element of $\{1, 2, 3\}$. The only elements of that set are 1, 2 and 3.
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HallsofIvy
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Of course, the empty set, $\phi$, is a subset of every set so it is true that $\phi\subset \{1, 2, 3\}$.
1. What is a circle?
A circle is a shape that is defined as a set of points that are all equidistant from a central point. It is a two-dimensional shape with no corners or edges.
2. How do I determine if a statement about circles is true?
In order to determine if a statement about circles is true, you must first understand the properties and characteristics of circles. Then, you can use mathematical principles and formulas to test the statement and see if it holds true for all circles.
3. Can a circle have a negative radius?
No, a circle cannot have a negative radius. A radius is defined as the distance from the center of a circle to any point on its circumference. Since distance cannot be negative, a circle's radius must always be a positive value.
4. Are all circles the same size?
No, not all circles are the same size. The size of a circle is determined by its radius or diameter, which can vary. Therefore, circles can have different sizes depending on these measurements.
5. Can a circle have a fractional radius?
Yes, a circle can have a fractional radius. In fact, many circles have fractional radii. For example, a circle with a radius of 1.5 units would have a diameter of 3 units. This is a common occurrence in geometry and mathematics.
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