समान समुच्चय - Revision history

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	'''हल:''' <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}=\{2,3,5,7\}</math>		'''हल:''' <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}=\{2,3,5,7\}</math>

	अब, <math>A</math> और <math>B</math> में ~~तत्वों~~ की संख्या समान है, अर्थात, <math>4</math> और सभी ~~तत्व~~ भी समान हैं।		अब, <math>A</math> और <math>B</math> में अवयवों की संख्या समान है, अर्थात, <math>4</math> और सभी अवयव भी समान हैं।

	अतः, <math>A=B</math>		अतः, <math>A=B</math>

Mani: added content

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← Older revision		Revision as of 16:36, 26 March 2024
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	(i) मान लीजिए <math>A=\{1,2,3,4\}</math> और <math>B=\{4,3,2,1\}</math>। तब <math>A=B</math>।		(i) मान लीजिए <math>A=\{1,2,3,4\}</math> और <math>B=\{4,3,2,1\}</math>। तब <math>A=B</math>।

	(ii) सिद्ध करें कि <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}</math> और <math>B=\{2,3,5,7\}</math>समान समुच्चय हैं।		(ii) सिद्ध करें कि <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}</math> और <math>B=\{2,3,5,7\}</math>समान समुच्चय हैं।

	'''हल:''' <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}=\{2,3,5,7\}</math>		'''हल:''' <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}=\{2,3,5,7\}</math>

	~~Now~~, ~~the number of elements in~~ <math>A</math> ~~and~~ <math>B</math> ~~are the same~~, ~~i.e.~~, <math>4</math> ~~and all the elements are also equal.~~		अब, <math>A</math> और <math>B</math> में तत्वों की संख्या समान है, अर्थात, <math>4</math> और सभी तत्व भी समान हैं।

	अतः, <math>A=B</math>		अतः, <math>A=B</math>

Mani: added content

2024-03-26T11:04:36Z

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← Older revision		Revision as of 16:34, 26 March 2024
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	== परिभाषा ==		== परिभाषा ==
	~~Two sets~~ <math>A</math> ~~and~~ <math>B</math> ~~are said to be equal if they have exactly the same elements and we write~~ <math>A=B</math>~~. Otherwise~~, ~~the sets are said to be unequal and we write~~ <math>A \neq B</math>.		दो समुच्चय <math>A</math> और <math>B</math> समान कहलाते हैं यदि उनके अवयव पूर्णतः समान हों और हम <math>A=B</math> लिखते हैं। अन्यथा, समुच्चयों को असमान कहा जाता है और हम<math>A \neq B</math> लिखते हैं।

	'''उदाहरण:'''		'''उदाहरण:'''

	(i) ~~Let~~ <math>A=\{1,2,3,4\}</math> ~~and~~ <math>B=\{4,3,2,1\}</math>~~. Then~~ <math>A=B</math>.		(i) मान लीजिए <math>A=\{1,2,3,4\}</math> और <math>B=\{4,3,2,1\}</math>। तब <math>A=B</math>।

	(ii) ~~Prove that~~ <math>A=\{x:x</math> ~~is prime such that~~ <math>1<x<10 \}</math> ~~and~~ <math>B=\{2,3,5,7\}</math>~~are equal sets.~~		(ii) सिद्ध करें कि <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}</math> और <math>B=\{2,3,5,7\}</math>समान समुच्चय हैं।

	'''हल:''' <math>A=\{x:x</math> ~~is prime such that~~ <math>1<x<10 \}=\{2,3,5,7\}</math>		'''हल:''' <math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}=\{2,3,5,7\}</math>

	Now, the number of elements in <math>A</math> and <math>B</math> are the same, i.e., <math>4</math> and all the elements are also equal.		Now, the number of elements in <math>A</math> and <math>B</math> are the same, i.e., <math>4</math> and all the elements are also equal.

	~~Therefore~~, <math>A=B</math>		अतः, <math>A=B</math>

	<math>A=\{x:x</math> ~~is prime such that~~ <math>1<x<10 \}=\{2,3,5,7\}=B</math>		<math>A=\{x:x</math> इस प्रकार अभाज्य है कि <math>1<x<10 \}=\{2,3,5,7\}=B</math>

	[[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]]		[[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]]

Mani: New Mathematics Class 11 Hindi Page Created

2024-03-26T10:53:06Z

New Mathematics Class 11 Hindi Page Created

← Older revision		Revision as of 16:23, 26 March 2024
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	~~Equal sets are sets in set theory in which the number of elements is the same and all elements are equal.~~		समुच्चय सिद्धांत में समान समुच्चय ऐसे समुच्चय हैं जिनमें अवयवों की संख्या समान होती है और सभी अवयव समान होते हैं।

	== ~~Definition~~ ==		== परिभाषा ==
	Two sets <math>A</math> and <math>B</math> are said to be equal if they have exactly the same elements and we write <math>A=B</math>. Otherwise, the sets are said to be unequal and we write <math>A \neq B</math>.		Two sets <math>A</math> and <math>B</math> are said to be equal if they have exactly the same elements and we write <math>A=B</math>. Otherwise, the sets are said to be unequal and we write <math>A \neq B</math>.

	'''~~Examples~~:'''		'''उदाहरण:'''

	(i) Let <math>A=\{1,2,3,4\}</math> and <math>B=\{4,3,2,1\}</math>. Then <math>A=B</math>.		(i) Let <math>A=\{1,2,3,4\}</math> and <math>B=\{4,3,2,1\}</math>. Then <math>A=B</math>.
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	(ii) Prove that <math>A=\{x:x</math> is prime such that <math>1<x<10 \}</math> and <math>B=\{2,3,5,7\}</math>are equal sets.		(ii) Prove that <math>A=\{x:x</math> is prime such that <math>1<x<10 \}</math> and <math>B=\{2,3,5,7\}</math>are equal sets.

	'''~~Solution~~:''' <math>A=\{x:x</math> is prime such that <math>1<x<10 \}=\{2,3,5,7\}</math>		'''हल:''' <math>A=\{x:x</math> is prime such that <math>1<x<10 \}=\{2,3,5,7\}</math>

	Now, the number of elements in <math>A</math> and <math>B</math> are the same, i.e., <math>4</math> and all the elements are also equal.		Now, the number of elements in <math>A</math> and <math>B</math> are the same, i.e., <math>4</math> and all the elements are also equal.

Mani at 10:50, 26 March 2024

2024-03-26T10:50:45Z

← Older revision		Revision as of 16:20, 26 March 2024
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	Equal ~~Sets~~		Equal sets are sets in set theory in which the number of elements is the same and all elements are equal.

			== Definition ==
			Two sets <math>A</math> and <math>B</math> are said to be equal if they have exactly the same elements and we write <math>A=B</math>. Otherwise, the sets are said to be unequal and we write <math>A \neq B</math>.

			'''Examples:'''

			(i) Let <math>A=\{1,2,3,4\}</math> and <math>B=\{4,3,2,1\}</math>. Then <math>A=B</math>.

			(ii) Prove that <math>A=\{x:x</math> is prime such that <math>1<x<10 \}</math> and <math>B=\{2,3,5,7\}</math>are equal sets.

			'''Solution:''' <math>A=\{x:x</math> is prime such that <math>1<x<10 \}=\{2,3,5,7\}</math>

			Now, the number of elements in <math>A</math> and <math>B</math> are the same, i.e., <math>4</math> and all the elements are also equal.

			Therefore, <math>A=B</math>

			<math>A=\{x:x</math> is prime such that <math>1<x<10 \}=\{2,3,5,7\}=B</math>

	[[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]]		[[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]]

Sarika at 06:12, 4 August 2023

2023-08-04T06:12:03Z

← Older revision		Revision as of 11:42, 4 August 2023
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	Equal Sets		Equal Sets

	[[Category:समुच्चय]][[Category:कक्षा-11]]		[[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]]

Sarika at 05:39, 4 August 2023

2023-08-04T05:39:21Z

← Older revision		Revision as of 11:09, 4 August 2023
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	Equal Sets		Equal Sets

	[[Category:समुच्चय]]		[[Category:समुच्चय]][[Category:कक्षा-11]]

Sarika at 11:59, 18 April 2023

2023-04-18T11:59:20Z

← Older revision		Revision as of 17:29, 18 April 2023
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	Equal Sets		Equal Sets
	~~[[Category:गणित]]~~
	[[Category:समुच्चय~~]][[Category: कक्षा-11~~]]		[[Category:समुच्चय]]

Sarika at 06:59, 21 March 2023

2023-03-21T06:59:34Z

← Older revision		Revision as of 12:29, 21 March 2023
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	Equal Sets		Equal Sets
	[[Category:गणित]]		[[Category:गणित]]
	[[Category:समुच्चय]]		[[Category:समुच्चय]][[Category: कक्षा-11]]

Mani: added category

2023-03-07T09:35:01Z

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← Older revision		Revision as of 15:05, 7 March 2023
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			[[Category:गणित]]
			[[Category:समुच्चय]]