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Nancy Rajput 7 years, 5 months ago

of which chapter
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Nancy Rajput 7 years, 5 months ago

every set is a subset of itself and the empty set is also the subset of every set it is known as improper subset
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Nancy Rajput 7 years, 5 months ago

(a + b)^2 = a^2 + b^2 + 2ab (a - b)^2 = a^2 + b^2 - 2ab So, a^2 + b^2 formula can be a^2 + b^2 = (a + b)^2 - 2ab a^2 + b^2 = (a - b)^2 + 2ab
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Nancy Rajput 7 years, 5 months ago

Proof of De Morgan’s law: (A ∩ B)' = A' U B' Let M = (A ∩ B)' and N = A' U B' Let x be an arbitrary element of M then x ∈ M ⇒ x ∈ (A ∩ B)' ⇒ x ∉ (A ∩ B) ⇒ x ∉ A or x ∉ B ⇒ x ∈ A' or x ∈ B' ⇒ x ∈ A' U B' ⇒ x ∈ N Therefore, M ⊂ N …………….. (i) Again, let y be an arbitrary element of N then y ∈ N ⇒ y ∈ A' U B' ⇒ y ∈ A' or y ∈ B' ⇒ y ∉ A or y ∉ B ⇒ y ∉ (A ∩ B) ⇒ y ∈ (A ∩ B)' ⇒ y ∈ M Therefore, N ⊂ M …………….. (ii) Now combine (i) and (ii) we get; M = N i.e. (A ∩ B)' = A' U B'

Nancy Rajput 7 years, 5 months ago

Proof of De Morgan’s law: (A U B)' = A' ∩ B' Let P = (A U B)' and Q = A' ∩ B' Let x be an arbitrary element of P then x ∈ P ⇒ x ∈ (A U B)' ⇒ x ∉ (A U B) ⇒ x ∉ A and x ∉ B ⇒ x ∈ A' and x ∈ B' ⇒ x ∈ A' ∩ B' ⇒ x ∈ Q Therefore, P ⊂ Q …………….. (i) Again, let y be an arbitrary element of Q then y ∈ Q ⇒ y ∈ A' ∩ B' ⇒ y ∈ A' and y ∈ B' ⇒ y ∉ A and y ∉ B ⇒ y ∉ (A U B) ⇒ y ∈ (A U B)' ⇒ y ∈ P Therefore, Q ⊂ P …………….. (ii) Now combine (i) and (ii) we get; P = Q i.e. (A U B)' = A' ∩ B'
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Yash Thakur 7 years, 5 months ago

9 elements A×A some order pair (-1,0) (0,1). Now we notice order pair that -1,0,1. Given elements are (-1,0)(0,1). A has three elements. A={-1,0,1} A×A = { -1,0,1}×{-1,0,1} Hence, remaining elements of A×A-- {(-1,0) (0,-1) (0,0) (1,-1) (-1,-1) (1,0) (1,1)}. ????

Nancy Rajput 7 years, 5 months ago

in last how remaining elements is find

Nancy Rajput 7 years, 5 months ago

expercise 2.1 question no 10 i cant understand it pls you explain me

Shivam Tiwari 7 years, 5 months ago

I am help you

Shivam Tiwari 7 years, 5 months ago

Yes iIcan help u
  • 1 answers

Suraj Thakur 7 years, 5 months ago

Lesson 2(c) qusiton no. 11 ka
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Nancy Rajput 7 years, 5 months ago

what we find in this question the value of Z or whay
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Nancy Rajput 7 years, 5 months ago

ohh sorry its (A union B)'

Mitesh Tiwari 7 years, 5 months ago

answer of nancy rajput was incorect

Nancy Rajput 7 years, 5 months ago

(A union B) =A' intersection B'

Mitesh Tiwari 7 years, 5 months ago

(A union B)'= A' intersection B'
  • 3 answers

Pammy Kumari 7 years, 5 months ago

-5 is correct answer

Nancy Rajput 7 years, 5 months ago

its -5

Lovely Dhawan 7 years, 5 months ago

-5
  • 4 answers

Vanisha Meena 7 years, 5 months ago

From starting

Prabhat Emmanuel 7 years, 5 months ago

U can take help from online lecture

Tapan Pandey 7 years, 5 months ago

Yeah

Arpit Pathak 7 years, 5 months ago

Which part dear
  • 2 answers

Khushi Singh 7 years, 5 months ago

Liyer you are talking in good english and saying that you have a problem

Anurag Parashar 7 years, 5 months ago

If you want to bcome an IT engineer then no prblm take CS in college But kahi aur s c++ ki language ka course kr lena that would help u
  • 1 answers

Neeraj Kumar 7 years, 5 months ago

A Set is a collection of things (usually numbers). Example: {5, 7, 11} is a set. But we can also "build" a set by describing what is in it. Here is a simple example of set-builder notation: It says "the set of all x's, such that x is greater than 0".
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Nancy Rajput 7 years, 5 months ago

we find all 6 trignometric
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Rachit Khandelwal 7 years, 5 months ago

Plz answer fast
  • 1 answers

Prabhat Emmanuel 7 years, 5 months ago

False because in equivalent set elements are not necessarily same.

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