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Ask QuestionPosted by Yashika Sachdeva 5 years, 1 month ago
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Posted by Payal Suryawanshi 5 years, 1 month ago
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Yogita Ingle 5 years, 1 month ago
All functions are relations, but not all relations are functions. Relations ...
Posted by Payal Suryawanshi 5 years, 1 month ago
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Posted by Payal Suryawanshi 5 years, 1 month ago
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Yogita Ingle 5 years, 1 month ago
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product set A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
The set of all first elements in a relation R is called the domain of the relation B, and the set of all second elements called images is called the range of R.
Posted by Akhifa Sheik 5 years, 1 month ago
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Yogita Ingle 5 years, 1 month ago
We know that if A is a set with m elements i.e., n(A)=m,
then, n[P(A)]=2m.
If A={} =ϕ, then n(A)=0
∴n[P(A)]=2o=1
Hence, P(A) has one element.
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?? 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
A/C to question,
9 + 12 + 15 + ....... n terms = 306
you can see that ,
common difference of the series is always equal to 3 . e.g (12 - 9) = (15 - 12) = 3
so, this series is in AP .
now,
Let total number of terms = n in such a way that sum of n terms = 306.
we know,
here, a = 9 , d = 3 and Sn = 306
now,
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Sehaj Gamer? 5 years, 1 month ago
Tec Om 5 years, 1 month ago
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 5 years, 1 month 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 5 years, 1 month 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 5 years, 1 month 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.
Posted by Saloni ? 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
Are A = {x : x – 5 = 0} and B = {x : x is a positive integral root of the equation x2 - 2x - 15} equal sets?
Answer:
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Gaurav Seth 5 years, 1 month ago
Q u e s t i o n : Find the number of different word that can be formed from the letter of the word intermediate such that two vowels never come together
A n s w e r is 1,51,200
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