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Mathematics Complement of a Set and its properties MCQ Questions for Class 11 General

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Complement of a Set and its properties Practice Questions

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Question 591/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), \(A=[-2,\infty\)) और (B=\(-\infty,5]\), तो (\(A'\cup B'\)') क्या है?

If \(U=\mathbb{R}\), \(A=[-2,\infty\)), and (B=\(-\infty,5]\), what is (\(A'\cup B'\)')?

Explanation opens after your attempt

Correct Answer

A. ([-2,5])

Explanation

Simple Explanation

डी मॉर्गन से (\(A'\cup B'\)'=A\cap B) है। \(A\cap B=[-2,5]\) मिलता है। / By De Morgan's law, (\(A'\cup B'\)'=A\cap B). Here \(A\cap B=[-2,5]\).

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Question 592/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,25}\), (A'={4,8,12,16,20,24}), तो (A) में (4) से विभाज्य कितने सदस्य हैं?

If \(U={1,2,\ldots,25}\) and (A'={4,8,12,16,20,24}), how many elements of (A) are divisible by (4)?

Explanation opens after your attempt

Correct Answer

A. (0)

Explanation

Simple Explanation

(4) से विभाज्य सभी सदस्य (A') में दिए गए हैं। इसलिए (A) में (4) से विभाज्य कोई सदस्य नहीं है। / All elements divisible by (4) are listed in (A'). Therefore (A) has no element divisible by (4).

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Question 593/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,15}\), \(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7,8\}\) और \(C=\{7,8,9,10\}\), तो (\(A\cup B\cup C\)') क्या है?

If \(U={1,2,\ldots,15}\), \(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7,8\}\), and \(C=\{7,8,9,10\}\), what is (\(A\cup B\cup C\)')?

Explanation opens after your attempt

Correct Answer

A. ({11,12,13,14,15})

Explanation

Simple Explanation

तीनों का संघ \({1,2,\ldots,10}\) है। (U) से हटाने पर ({11,12,13,14,15}) बचता है। / The union of the three sets is \({1,2,\ldots,10}\). Removing it from (U) leaves ({11,12,13,14,15}).

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Question 594/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,54}\), \(A={x:x\in U,6\mid x}\), \(B={x:x\in U,9\mid x}\), तो (n\(A'\cap B\)) क्या है?

If \(U={1,2,\ldots,54}\), \(A={x:x\in U,6\mid x}\), and \(B={x:x\in U,9\mid x}\), what is (n\(A'\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (3)

Explanation

Simple Explanation

(B) में (9,18,27,36,45,54) हैं। इनमें (18,36,54) (6) से विभाज्य हैं, इसलिए \(A'\cap B\) में (9,27,45) यानी (3) सदस्य हैं। / (B) contains (9,18,27,36,45,54). Among them (18,36,54) are divisible by (6), so \(A'\cap B\) has (9,27,45), that is (3) elements.

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Question 595/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\) और \(A={x:x\in\mathbb{R},x^2=4}\), तो (A') क्या है?

If \(U=\mathbb{R}\) and \(A={x:x\in\mathbb{R},x^2=4}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. \(\mathbb{R}-{-2,2}\)

Explanation

Simple Explanation

\(x^2=4\) से (x=-2) या (x=2) मिलता है। इसलिए पूरक \(\mathbb{R}-{-2,2}\) है। / \(x^2=4\) gives (x=-2) or (x=2). Therefore the complement is \(\mathbb{R}-{-2,2}\).

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Question 596/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि (n(U)=75), (n(A)=28), (n(B)=35) और (n\(A\cup B\)=50), तो (n(\(A'\cap B'\)')) क्या है?

If (n(U)=75), (n(A)=28), (n(B)=35), and (n\(A\cup B\)=50), what is (n(\(A'\cap B'\)'))?

Explanation opens after your attempt

Correct Answer

A. (50)

Explanation

Simple Explanation

डी मॉर्गन से (A'\cap B'=\(A\cup B\)') है। इसलिए (\(A'\cap B'\)'=A\cup B), जिसकी संख्या (50) है। / By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Hence (\(A'\cap B'\)'=A\cup B), whose cardinality is (50).

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Question 597/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,22}), (A={x:x\in U,x\) सम है\(}), (B={x:x\in U,x\) पूर्ण वर्ग है\(}), तो ((A\cap B)') क्या है\)?

\(If (U={1,2,\ldots,22}), (A={x:x\in U,x\) is even\(}), and (B={x:x\in U,x\) is a perfect square\(}), what is ((A\cap B)')\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22})

Explanation

Simple Explanation

\(A\cap B\) में सम पूर्ण वर्ग (4) और (16) हैं। इन्हें (U) से हटाने पर पूरक मिलता है। / \(A\cap B\) contains even perfect squares (4) and (16). Removing them from (U) gives the complement.

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Question 598/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,81}\), \(A={x:x\in U,3\mid x}\) और \(B={x:x\in U,27\mid x}\), तो \(B'\cap A\) में कितने सदस्य हैं?

If \(U={1,2,\ldots,81}\), \(A={x:x\in U,3\mid x}\), and \(B={x:x\in U,27\mid x}\), how many elements are in \(B'\cap A\)?

Explanation opens after your attempt

Correct Answer

A. (24)

Explanation

Simple Explanation

(A) में (3) के (27) गुणज हैं और (B) में (27) के (3) गुणज हैं। इसलिए \(B'\cap A\) में (27-3=24) सदस्य हैं। / (A) has (27) multiples of (3), and (B) has (3) multiples of (27). Hence \(B'\cap A\) has (27-3=24) elements.

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Question 599/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), (A=\(-\infty,-1]\cup[6,\infty\)), तो ((A')') क्या है?

If \(U=\mathbb{R}\), (A=\(-\infty,-1]\cup[6,\infty\)), what is ((A')')?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,-1]\cup[6,\infty\))

Explanation

Simple Explanation

द्वि-पूरक नियम के अनुसार ((A')'=A) होता है। इसलिए उत्तर वही मूल समुच्चय है। / By the double complement law, ((A')'=A). Therefore the answer is the original set itself.

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Question 600/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{N},x\le 90}\), \(A={x:x\in U,10\mid x}\), \(B={x:x\in U,18\mid x}\), तो (n\(A'\cap B'\)) क्या है?

If \(U={x:x\in\mathbb{N},x\le 90}\), \(A={x:x\in U,10\mid x}\), and \(B={x:x\in U,18\mid x}\), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (77)

Explanation

Simple Explanation

(A'\cap B'=\(A\cup B\)') है। (n\(A\cup B\)=9+5-1=13), इसलिए पूरक (90-13=77) है। / (A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=9+5-1=13), the complement is (90-13=77).

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Mathematics Complement of a Set and its properties MCQ Questions for Class 11 General

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Complement of a Set and its properties Practice Questions

यदि \(U=\mathbb{R}\), \(A=[-2,\infty\)) और (B=\(-\infty,5]\), तो (\(A'\cup B'\)') क्या है?

Simple Explanation

यदि \(U={1,2,\ldots,25}\), (A'={4,8,12,16,20,24}), तो (A) में (4) से विभाज्य कितने सदस्य हैं?

Simple Explanation

यदि \(U={1,2,\ldots,15}\), \(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7,8\}\) और \(C=\{7,8,9,10\}\), तो (\(A\cup B\cup C\)') क्या है?

Simple Explanation

यदि \(U={1,2,\ldots,54}\), \(A={x:x\in U,6\mid x}\), \(B={x:x\in U,9\mid x}\), तो (n\(A'\cap B\)) क्या है?

Simple Explanation

यदि \(U=\mathbb{R}\) और \(A={x:x\in\mathbb{R},x^2=4}\), तो (A') क्या है?

Simple Explanation

यदि (n(U)=75), (n(A)=28), (n(B)=35) और (n\(A\cup B\)=50), तो (n(\(A'\cap B'\)')) क्या है?

Simple Explanation

\(यदि (U={1,2,\ldots,22}), (A={x:x\in U,x\) सम है\(}), (B={x:x\in U,x\) पूर्ण वर्ग है\(}), तो ((A\cap B)') क्या है\)?

Simple Explanation

यदि \(U={1,2,\ldots,81}\), \(A={x:x\in U,3\mid x}\) और \(B={x:x\in U,27\mid x}\), तो \(B'\cap A\) में कितने सदस्य हैं?

Simple Explanation

यदि \(U=\mathbb{R}\), (A=\(-\infty,-1]\cup[6,\infty\)), तो ((A')') क्या है?

Simple Explanation

यदि \(U={x:x\in\mathbb{N},x\le 90}\), \(A={x:x\in U,10\mid x}\), \(B={x:x\in U,18\mid x}\), तो (n\(A'\cap B'\)) क्या है?

Simple Explanation

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Mathematics Complement of a Set and its properties MCQ Questions for Class 11 General

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Complement of a Set and its properties Practice Questions

यदि \(U=\mathbb{R}\), \(A=[-2,\infty\)) और (B=\(-\infty,5]\), तो (\(A'\cup B'\)') क्या है?

Simple Explanation

यदि \(U={1,2,\ldots,25}\), (A'={4,8,12,16,20,24}), तो (A) में (4) से विभाज्य कितने सदस्य हैं?

Simple Explanation

यदि \(U={1,2,\ldots,15}\), \(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7,8\}\) और \(C=\{7,8,9,10\}\), तो (\(A\cup B\cup C\)') क्या है?

Simple Explanation

यदि \(U={1,2,\ldots,54}\), \(A={x:x\in U,6\mid x}\), \(B={x:x\in U,9\mid x}\), तो (n\(A'\cap B\)) क्या है?

Simple Explanation

यदि \(U=\mathbb{R}\) और \(A={x:x\in\mathbb{R},x^2=4}\), तो (A') क्या है?

Simple Explanation

यदि (n(U)=75), (n(A)=28), (n(B)=35) और (n\(A\cup B\)=50), तो (n(\(A'\cap B'\)')) क्या है?

Simple Explanation

\(यदि (U={1,2,\ldots,22}), (A={x:x\in U,x\) सम है\(}), (B={x:x\in U,x\) पूर्ण वर्ग है\(}), तो ((A\cap B)') क्या है\)?

Simple Explanation

यदि \(U={1,2,\ldots,81}\), \(A={x:x\in U,3\mid x}\) और \(B={x:x\in U,27\mid x}\), तो \(B'\cap A\) में कितने सदस्य हैं?

Simple Explanation

यदि \(U=\mathbb{R}\), (A=\(-\infty,-1]\cup[6,\infty\)), तो ((A')') क्या है?

Simple Explanation

यदि \(U={x:x\in\mathbb{N},x\le 90}\), \(A={x:x\in U,10\mid x}\), \(B={x:x\in U,18\mid x}\), तो (n\(A'\cap B'\)) क्या है?

Simple Explanation

Complement of a Set and its properties Learning Links

Sets Chapter

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