Set (Types)

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Overlapping and Disjoint Set

सार्क राष्ट्रहरू अन्तर्गत पर्ने देशहरूमध्ये केही राष्ट्रहरू समुद्रसँग जोडिएका छन् भने केही राष्ट्रहरू भूपरिवेष्टित छन। यसलाई समूहमा बिभिन्न तरिकाले जनाउन सकिन्छ । जस्तै
A={समुद्रसँग जोडिएका राष्ट्रहरू}
B={भूपरिवेष्टित राष्ट्रहरू}
C={भारतसँग सिमा जोडिएका राष्ट्रहरू}
दिइएको नक्शा अध्ययन गरी \(A,B\) र \(A,C\) लाई समूहमा कसरी जनाउन सकिन्छ बिचार गर्नुहोस? यि दुबैको भेन चित्र Overlapping वा Disjoint के हुन्छ? तलको भेन चित्रमा तयार गर्नुहोस।

Drag and Drop Quiz: Q1

Look at the map above and, drag each country to all correct categories it belongs to. Please note that some countries belong to more than one group!

A: Sea Access

B: Landlocked

C: Borders India

Score: 0 / 12

सार्क राष्ट्रहरू अन्तर्गत पर्ने देशहरूमध्ये केही राष्ट्रहरू समुद्रसँग जोडिएका छन् भने केही राष्ट्रहरू भूपरिवेष्टित छन। यसलाई समूहमा बिभिन्न तरिकाले जनाउन सकिन्छ । जस्तै
A={समुद्रसँग जोडिएका राष्ट्रहरू}
B={भूपरिवेष्टित राष्ट्रहरू}
C={भारतसँग सिमा जोडिएका राष्ट्रहरू}
यि समूहको भेन चित्र Overlapping वा Disjoint के हुन्छ?

In this activity,
the sets A and B are
Overlapping Disjoint
the sets A and C are
Overlapping Disjoint

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Overlapping Set

कुनै दुई वा दुईभन्दा बढी समूहमा कम्तीमा एउटा साझा सदस्य र कम्तीमा एउटा फरक सदस्य छ भने त्यस्ता समूहलाई खप्टिएका समूह (Overlapping Set) भनिन्छ ।
जस्तै,
यदि \( A = \{1,2,3\} \) र \( B = \{3,4,5\} \) छन् भने \( A \) र \( B \) खप्टिएको समुह हो किनभने \(\{3\}\) दुबैमा साझा सदस्य हो। चित्र [overlappingset] हेर्नुहोस्।

Disjoint Set

कुनै दुई वा दुईभन्दा बढी समूहमा कुनै पनि साझा सदस्य छैनन् भने त्यस्ता समूहलाई अलग्गिएका समूह (Disjoint Set) भनिन्छ । जस्तै, यदि \( A = \{1, 2, 3\} \) र \( B = \{4, 5, 6\} \) छन् भने \( A \) र \( B \) परस्पर अलग्गिएका समुह हुन् किनभने तिनीहरूमा कुनै पनि साझा सदस्य छैन। चित्र [disjointset] हेर्नुहोस्।

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दिइएको भेनचित्र अध्ययन गरी समूह M र N लाई सूचीकरण तथा व्याख्या विधिबाट लेख्नुहोस्।

सूचीकरणविधि अनुसार
\(M=\)
\(N=\)
व्याख्या विधि अनुसार
\(M=\)
\(N=\)

सूचीकरणविधि अनुसार
\(M=\{3,,6,9,12,15\}\)
\(N=\{6,12,18,24\}\)
व्याख्या विधि अनुसार
\(M=\) set of the first five positive multiples of 3.
\(N=\) set of the first four positive multiples of 6.

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सर्वव्यापक समूह U का तिनवटा उपसमूहहरु \(P, Q\) र \(R\) छन्। यदि
U ={20 सम्मका 2 को अपवर्त्य हो ।}
P ={10 का गुणनखण्डहरू}
Q ={5 का अपवर्त्य हो ।} हो। र
R ={6 का अपवर्त्य हो ।}
अब, \(P,Q\) तथा \(Q, R\) लाई भेनचित्रमा प्रस्तुत गर्नुहोस्। साथै \(P,Q\) तथा \(Q,R\) को सम्बन्ध पनि उल्लेख गर्नुहोस।

सर्वव्यापक समूह \( U \) र उपसमूहहरू \( P, Q, R \) को परिभाषा अनुसार
\( U = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\} \)
\( P = \{1, 2, 5, 10\} \cap U = \{2, 10\} \)
\( Q = \{5, 10, 15, 20, \dots\} \cap U = \{10, 20\} \)
\( R = \{6, 12, 18, 24, \dots\} \cap U = \{6, 12, 18\} \)

\( P \) र \( Q \) को सम्बन्ध

Here
\( P \cap Q = \{10\} \)
Therefore, \( P \) र \( Q \) are overlaping sets.

\( Q \) र \( R \) को सम्बन्ध

Here
\( Q \cap R = \emptyset \)
Therefore, \( Q \) र \( R \) are disjoint sets.

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If \( M = \{x : x \text{ is a multiple of 5 less than 40} \} \), list out the elements of the following sets.

1. Set \( N \) is formed by adding 3 to each element of the set \( M \).
2. Set \( P \) is formed by multiplying each element of set \( M \) by 2.
3. Set \( Q \) is formed by collecting all the odd numbers of set \( M \).
4. Set \( R \) is formed by collecting the multiples of 10 from set \( M \).
5. Write the Universal set for the sets given above.
6. Identify the overlapping and disjoint sets among sets \( M, N, P, Q, \) and \( R \).
   

Given that
\( M = \{5, 10, 15, 20, 25, 30, 35\} \)

1. Set \( N \) is formed by adding 3 to each element of \( M \), so
   \( N = \{5+3, 10+3, 15+3, 20+3, 25+3, 30+3, 35+3\} = \{8, 13, 18, 23, 28, 33, 38\} \)
2. Set \( P \)is formed by multiplying each element of \( M \) by 2, so
   \( P = \{2 \times 5, 2 \times 10, 2 \times 15, 2 \times 20, 2 \times 25, 2 \times 30, 2 \times 35\} = \{10, 20, 30, 40, 50, 60, 70\} \)
3. Set \( Q \)is formed by collecting all the odd numbers of \( M \), so
   \( Q = \{5, 15, 25, 35\} \)
4. Set \( R \) is formed by collecting the multiples of 10 from \( M \), so
   \( R = \{10, 20, 30\} \)
5. Universal set \( U \) for the sets \( M, N, P, Q, R \) is
   \( U = M \cup N \cup P \cup Q \cup R \)
   or\( U = \{5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 33, 35, 38, 40, 50, 60, 70\} \)
6. Overlapping and Disjoint Sets

Identify whether each pair of sets is Overlapping (O) or Disjoint (D)

Pair	Overlapping (O)	Disjoint (D)
\( M \) and \( Q \)
\( M \) and \( R \)
\( P \) and \( R \)
\( M \) and \( P \)
\( M \) and \( N \)
\( N \) and \( P \)
\( N \) and \( Q \)
\( N \) and \( R \)
\( Q \) and \( R \)

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If \(U = \{\text{the set of natural numbers up to } 20\}\)

1. \(A = \{\text{the set of even numbers up to } 10\}\)
2. \(B = \{\text{the set of odd numbers up to } 10\}\)
3. \(C = \{\text{the set of prime numbers up to } 10\}\)
4. \(D = \{\text{multiples of 2}\}\).

Specify if the given sets are disjoint or overlap in a table below. Write \(D\) if disjoint, \(O\) if overlapping, \(E\) if equal and \(NA\) if not applicable. Also represent them in separate Venn diagram.

Now,sSelect the correct relationship for each pair:

	A	B	C	D
A	--DOENA	--DOENA	--DOENA	--DOENA
B	--DOENA	--DOENA	--DOENA	--DOENA
C	--DOENA	--DOENA	--DOENA	--DOENA
D	--DOENA	--DOENA	--DOENA	--DOENA

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Prepare a universal set consisting of your family members and do the following work:

1. \(A=\) set of members of your family who likes bread as their breakfast.
2. \(B=\) set of members of your family who likes other breakfast.
3. Represent \(A\) and \(B\) in venn-diagram

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Equal and Equivalent Set

दुई वा बढी समुहहरूमा समान र उही सदस्यहरू छन् भने त्यस्तो समुहहरूलाई बराबर समुह भनिन्छ। जस्तै,
यदि \( A = \{1, 2\}, B = \{2, 1\}, C = \{12\} \) र \( D = \{21\} \) छन् भने
\( A = B \) तर \( C \ne D \) बराबर समुहको संकेत (\(=\)) हो।
दुई वा बढी समुहहरूमा समान सँख्यमा सदस्यहरू छन् भने त्यस्तो समुहहरूलाई समतुल्य समुह भनिन्छ। जस्तै,
यदि \( A = \{1, 2, 3\} \) र \( B = \{p, q, r\} \) छन् भने
\( A \sim B \) समतुल्य समुहको संकेत (\(\sim\)) हो।