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What is a partition in discrete mathematics?
First you must understand the term of disjoint sets. This is when both sets have no elements in common.Ex: A={2,3,4} B={1,5,9}. Since A has no similar numbers in B and likewise, they are disjoint.A is a partition of a finite or infinite collection of nonempty sets G= {A,B,C,D...},Iff:1) A is in the union of all {A,B,C,D...}2) The sets A,B,C,D...are all mutually disjoint (no overlapping of elements)So in other words, A=/B=/C=/D=/... ---(=/ is 'does not equal')---i.e. (A intersect B) = {} ---- ({} is an empty set)---
Can two disjoint sets be equivalent?
Yes,Because not all disjoint no equivalent other have disjoint and equivalent
What is a joint sets and disjoint sets?
Joint sets:Joint sets are those which have common elements Disjoint sets : A pair of sets is said to be disjoint if their intersection is the empty set. That is to say, if they share no elements. All of the usual operations can be performed on disjoint sets, so long as the operation makes sense. (For example, taking the complement of one with respect to the other could pose problems.)
What is the symbol for joint sets?
There is no such symbol for joint sets. Actually, there is a representation for joint sets. That is: The sets are joint if A ∩ B is not empty. The sets are disjoint if A ∩ B is empty.
What is the argument that A equals B B equals C so A equals C?
A=B , A-B=B-B , A-B =0 B=C , B-B=C-B, 0=C-B So A-B=0 but also C-B=0 A-B=C-B ...add +b ...A-B+B=C-B+B , A=C
What is the probability of Aor B if and B are disjoint?
1
What is a partition in discrete mathematics?
First you must understand the term of disjoint sets. This is when both sets have no elements in common.Ex: A={2,3,4} B={1,5,9}. Since A has no similar numbers in B and likewise, they are disjoint.A is a partition of a finite or infinite collection of nonempty sets G= {A,B,C,D...},Iff:1) A is in the union of all {A,B,C,D...}2) The sets A,B,C,D...are all mutually disjoint (no overlapping of elements)So in other words, A=/B=/C=/D=/... ---(=/ is 'does not equal')---i.e. (A intersect B) = {} ---- ({} is an empty set)---
If A and B are disjoint sets and A contains 5 elements and B contains 7 how many elements are in the union of A and B?
Disjoint means they have no elements in common. The union is the set of elements containing all elements from both sets. Since there is no overlap, the union will have 5+7 elements. Therefore the answer is 12.
Event A has probability 0.4 event B has probability 0.5 If A and B are disjoint then the probability that both events occur is?
If two events are disjoint, they cannot occur at the same time. For example, if you flip a coin, you cannot get heads AND tails. Since A and B are disjoint, P(A and B) = 0 If A and B were independent, then P(A and B) = 0.4*0.5=0.2. For example, the chances you throw a dice and it lands on 1 AND the chances you flip a coin and it land on heads. These events are independent...the outcome of one event does not affect the outcome of the other.
Addition rule for probability of events A and B?
If they're disjoint events: P(A and B) = P(A) + P(B) Generally: P(A and B) = P(A) + P(B) - P(A|B)
What is an example of a disjoint set?
The good real life example is the box of toys and the box of food. Imagine letting A be the box of toys and B be the box of food. Then, the intersection of those sets is empty.The example of disjoint set in mathematics is as followed:Let A = {1,2} and B = {3}. Then, A ∩ B = ∅
Can two disjoint sets be equivalent?
Yes,Because not all disjoint no equivalent other have disjoint and equivalent
What is joint and disjoint?
Two sets are said to be "disjoint" if they have no common element - their intersection is the empty set. As far as I know, "joint" is NOT used in the sense of the opposite of disjoint, i.e., "not disjoint".
What is a joint sets and disjoint sets?
Joint sets:Joint sets are those which have common elements Disjoint sets : A pair of sets is said to be disjoint if their intersection is the empty set. That is to say, if they share no elements. All of the usual operations can be performed on disjoint sets, so long as the operation makes sense. (For example, taking the complement of one with respect to the other could pose problems.)
What is disjoint?
A disjoint event is an event that can not happen at the same time
What is joint and disjoint set?
Two sets are said to be "disjoint" if they have no common element - their intersection is the empty set. As far as I know, "joint" is NOT used in the sense of the opposite of disjoint, i.e., "not disjoint".
What is a disjoint set?
ExplanationFormally, two sets A and B are disjoint if their intersection is the empty set, i.e. if This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint andSets that are not the same.
