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(a) Define power set, null set, …

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(a) Define power set, null set, universal set and subset (b) Write the following in set builder form (i) [6,12] , (ii) [−23,5)
  • 5 answers

Sehaj Gamer? 4 years, 5 months ago

See this definition in ur maths ncert book u will find all definition with examples ??

Tec Om 4 years, 5 months ago

power set is the set with all possible subsets denoted by p(a) where a is any other set.
universal set is the set which contain all subsets of other sets and it is denoted by U.
A subset is a set which contain elements of other set.
nullset or empty set does not contain any element
(i)A={x:x is the multiple of 0 <x>18}

Gaurav Seth 4 years, 5 months ago

Any Set that does not contain any element is called the empty or null or void set. The symbol used to represent an empty set is – {} or φ. Examples:

  • Let A = {x : 9 < x < 10, x is a natural number} will be a null set because there is NO natural number between numbers 9 and 10. Therefore, A = {} or φ
  • Let W = {d: d > 8, d is the number of days in a week} will also be a void set because there are only 7 days in a week.

Gaurav Seth 4 years, 5 months ago

A universal set is a set which contains all the elements or objects of other sets, including its own elements. It is usually denoted by the symbol ‘U’.

Suppose Set A consist of all even numbers such that, A = {2, 4, 6, 8, 10, …} and set B consist of all odd numbers, such that, B = {1, 3, 5, 7, 9, …}. The universal set U consist of all natural numbers, such that, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,….}. Therefore, as we know, all the even and odd numbers are a part of natural numbers. Therefore, Set U has all the elements of Set A and Set B.

Gaurav Seth 4 years, 5 months ago

The power set is a set which includes all the subsets including the empty set and the original set itself. It is also a type of sets. If set A = {x,y,z} is a set, then all its subsets {x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z} and {} are the elements of powerset, such as:

Power set of A, P(A) = {x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z} and {}

Where P(A) denotes the powerset.

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