Show that the following four conditions are equivalent:
(i) A ⊂ B (ii) A - B = Φ (iii) A ∪ B = B (iv) A ∩ B = A
AnswerFirst, we shall try to prove A ⊂ B ⇔ A - B = Φ
Given A ⊂ B
To prove A - B = Φ
A ⊂ B so that A ∩ B = A
LHS
=A - B
= A – (A ∩ B)
= A-A
= Φ
RHS
Given A - B = Φ
To prove A ⊂ B
Let x ∈ A
Given that A - B = Φ so all element of A must be in set B
Therefore, x ∈ B
So that A ⊂ B
Hence proved
Similarly you can solve all other parts.
I Found another site for such solutions ! NCERT Solutions
ReplyDeleteBut B is not equal to A intersecti
ReplyDeleteon B
How (iv) is equivalent to others?
ReplyDelete
ReplyDeleteNCERT Solutions, CBSE Sample Papers and Syllabus for Class 9 to 12
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Tuesday, 15 April 2014
Show that the following four conditions are equivalent: (i) A ⊂ B (ii) A - B = Φ (iii) A ∪ B = B (iv) A ∩ B = A
Show that the following four conditions are equivalent:
(i) A ⊂ B (ii) A - B = Φ (iii) A ∪ B = B (iv) A ∩ B = A
Answer
First, we shall try to prove A ⊂ B ⇔ A - B = Φ
Given A ⊂ B
To prove A - B = Φ
A ⊂ B so that A ∩ B = A
LHS
=A - B
= A – (A ∩ B)
= A-A
= Φ
RHS
Given A - B = Φ
To prove A ⊂ B
Let x ∈ A
Given that A - B = Φ so all element of A must be in set B
Therefore, x ∈ B
So that A ⊂ B
Hence proved
Similarly you can solve all other parts.
Unknown at 00:12
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4 comments:
sahid ansari9 July 2017 at 04:12
Koi h
Reply
harshit raj25 December 2017 at 02:01
I Found another site for such solutions ! NCERT Solutions
Reply
Unknown24 July 2018 at 10:21
But B is not equal to A intersecti
on B
Reply
Unknown20 September 2018 at 09:58
How (iv) is equivalent to others?
Reply
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