1. A universal set (usually denoted by U) is a set which has elements of all the related sets, without any repetition of elements. Universal set contains a group of objects or elements which are available in all the sets and is represented in a Venn diagram.
2. A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
3. The union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero () sets and it is by definition equal to the empty set.
4. In set theory, the complement of a set A, often denoted by Ac (or A′), are the elements not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U that are not in A.
5. The function difference() returns a set that is the difference between two sets. Let's try to find out what will be the difference between two sets A and B. Then (set A – set B) will be the elements present in set A but not in B and (set B – set A) will be the elements present in set B but not in set A.
6. To visualize set operations, we will use Venn diagrams. In a Venn diagram, a rectangle shows the universal set, and all other sets are usually represented by circles within the rectangle. The shaded region represents the result of the operation.
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Answer:
1. A universal set (usually denoted by U) is a set which has elements of all the related sets, without any repetition of elements. Universal set contains a group of objects or elements which are available in all the sets and is represented in a Venn diagram.
2. A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
3. The union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero () sets and it is by definition equal to the empty set.
4. In set theory, the complement of a set A, often denoted by Ac (or A′), are the elements not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U that are not in A.
5. The function difference() returns a set that is the difference between two sets. Let's try to find out what will be the difference between two sets A and B. Then (set A – set B) will be the elements present in set A but not in B and (set B – set A) will be the elements present in set B but not in set A.
6. To visualize set operations, we will use Venn diagrams. In a Venn diagram, a rectangle shows the universal set, and all other sets are usually represented by circles within the rectangle. The shaded region represents the result of the operation.
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