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Is intersection of two countably infinite sets can be finite?
Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.
Is the set of points two or more figures have in common?
Their intersection.
What is the intersection of two distinct planes?
The intersection of two distinct planes is a line. The set of common points in the line lies in both planes.
If the graphs of two linear equations in a system have the same slope the system has what kind of solution?
If they have the same slope, then there are two possibilities. First say they have the same slope and different y intercepts. This means they are parallel lines and there is no intersection. The solution is the empty set or we say there is no solution.If the y intercept is the same, then the two equations represent the same line. In this case there is an infinite number of solutions.
What is a set of points that two or more plane figures have in common?
Intersection
Why empty set is a set?
The concept of closure: If A and B are sets the intersection of sets is a set. Then if the intersection of two sets is a set and that set could be empty but still a set. The same for union, a set A union set Null is a set by closure,and is the set A.
Is intersection of two countably infinite sets can be finite?
Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.
Do sets always have an intersection that is not the empty set?
No, they do not.
Is The intersection of two nonempty sets is always nonempty?
Not necessarily. The odd integers and the even integers are two infinitely large sets. But their intersection is the null (empty) set.
What is the intersection of two nonparallel lines in space?
In Euclidea space it is either a point or the two lines - which must be coincident. ----- Intersection = the point/s where the two lines meet in space. It is a point or set of points that are common to two or more geometric configurations (also called "product" - the set of elements that are common to two sets).
How will you write using the venn diagram the union of set a(1234) and the intersection of set b(10111213) and set c(1213)?
If B = {10111213} and C = {1213} then their intersection is the empty set, {}.The union of A with an empty set is set A.
What is the intersection of two disjoint sets?
Because they are disjoint, (ie. they contain none of the same elements) their intersection (what they both share in common) is the empty or null set.
Is the intersection of any two half-planes necessarily a half-plane?
In general no. The intersection of two parallel half-planes A and B is either a half-plane (either A or B, when A and B have similar orientation) or the empty set (when A and B have opposite orientation). When A and B are not parallel, their intersection is a maximal open region bounded by the two lines that define A and B, respectively. In this case, the intersection always exists and it is never a half-plane.
What is interseting set?
I presume you mean intersecting. Two sets are intersecting if they have members in common. The set of members common to two (or more) sets is called the intersection of those sets. If two sets have no members in common, their intersection is the empty set. In this case the sets are called disjoint.
How do you sketch a set of lines that has two points of intersection?
They can be two arcs, like the outline of a crescent moon, or a contact lens. Two straight lines on a plane surface cannot have two points of intersection: there can only be 0, 1 or infinitely many.
What is intersection of the set?
You normally do not have an intersection of only one set. The intersection of a set with itself is the set itself - a statement that adds little value. The intersection of two sets is the set which contains elements that are in each of the two sets.
Is the union of disjoint sets is always the empty set?
No, only if both sets are empty. The intersection of disjoint sets is always empty.
