NCERT/CBSE MATHEMATICS CLASS 11 textbook - TutorBreeze.com

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NCERT/CBSE MATHEMATICS CLASS 11 textbook http://www.TutorBreeze.com. Please do not copy the answer given here. Write to us for help.
NCERT/CBSE MATHEMATICS CLASS 11 textbook http://www.TutorBreeze.com MISCELLANEOUS EXERCISES Answers to NCERT/CBSE MATH (Class XI)textbook SETS

Solution: We will show that : (i) A ⊂ B ⇒ A - B = φ (ii) A ⊂ B (iii) A ⊂ B

⇒ A∪ B =B ⇒A∩B = A

Thus implying that all four conditions are equivalent (i)

Let x be any element of A , i.e x ∈ A A ⊂ B

(given )

⇒ x∈ B ⇒Every element of set A is an element of set B ⇒ A - B = φ Therefore , A ⊂ B

⇒ A - B = φ

(ii) A ∪ B = { x : x ∈ A or x ∈ B} But here A ⊂ B A ∪ B = { x : x ∈ B or x ∈ B} = B

Therefore ,

A ⊂ B ⇒ A∪ B =B

(iii) A ∩ B = { x : x ∈ A and x∈ B} But here A ⊂ B Please do not copy the answer given here Write to us for help

NCERT/CBSE MATHEMATICS CLASS 11 textbook http://www.TutorBreeze.com

A ∩ B = { x : x ∈ A and x∈ A} = A Therefore, all four conditions are equivalent

Please do not copy the answer given here Write to us for help