Question

Define the following(Chapter-Set)

a)Sub-set
b)Proper sub-set
c)Super-set
d)Power set
e)Universal set​

Answer 1

Answer:

a)a set of which all the elements are contained in another set.

b) Set A is considered to be a proper subset of Set B if Set B contains at least one element that is not present in Set A.

c) A set A is a superset of another set B if all elements of the set B are elements of the set A

d) a power set includes all the subsets of a given set including the empty set. The power set is denoted by the notation P

e) the set containing all objects or elements and of which all other sets are subsets

Step-by-step explanation:

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Answer 2

Answer:

1. Since a set is a well – defined collection of objects or elements grouped together within braces {}, it can also be disintegrated into smaller sets of its own called the subsets. Mathematically, a set A is referred to as the subset of another set B, if every element of set A is also an element of set B.

2. If set A has all its elements present in set B and set B has more number of elements then set A is a proper set of set B. The proper set is represented as ‘⊂’ 

f set A has all its elements present in set B and set B has more number of elements then set A is a proper set of set B. The proper set is represented as ‘⊂’ Two sets having an equal number of elements can never be proper sets of each other, hence, a set is never a proper set of itself.

3. Supersets are those sets which are defined by the following conditions: A ⊂ B and A ≠ B. When these two conditions are fulfilled, B is called a superset of set A. Supersets are represented by the symbol which is the mirror image of the symbol used to represent a subset: B ⊃ A          {B is the superset of A}

4. Power Set is defined as the set of all the possible subsets of the given set. The definition seems a little confusing but in real, Power sets are very easily understood. Imagine a set with some elements present in them, now write all the possible subsets that can be written for the particular set, treat the subsets as elements as place them in a separate set, this set obtained will be called as a Power set.

5. Universal set is the master of all the sets, that is, it contains all the elements present in all the sets given. The universal set is represented as U, and it is represented as a rectangle in the Venn diagram, all the other sets are drawn within the rectangle, this is done to show that the universal set contains all the possible elements.

Step-by-step explanation:

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