Partition

Class 12 Mathematics के इस tag से जुड़े questions।

Class 12 · Mathematics

If R is an equivalence relation on a set A, which statement about its equivalence classes is correct?

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Class 12 · Mathematics

On (A={1,2,3,4,5,6}), relation (R) has classes ({1,6}), ({2,3,5}), and ({4}). Which pair definitely will not be in (R)?

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Class 12 · Mathematics

On (A={1,2,3,4,5,6,7,8}), (aRb) if (a) and (b) lie in the same block among ({1,2}), ({3,4,5}), ({6,7,8}). How many pairs are in the relation?

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Class 12 · Mathematics

If two equivalence classes ([a]) and ([b]) of an equivalence relation are distinct, what is true about their intersection?

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Class 12 · Mathematics

On (A={1,2,3,4,5}), one equivalence class of (R) is ({1,2,5}). If (R) is an equivalence relation, which pair cannot be in (R)?

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Class 12 · Mathematics

On (A={1,2,3,4}), the equivalence classes are ({1,4}) and ({2,3}). Which pair must belong to the relation?

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Class 12 · Mathematics

A partition of (A={1,2,3,4,5}) is ({{1,3,5},{2,4}}). How many ordered pairs will be in the equivalence relation formed by this partition?

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Class 12 · Mathematics

If (R) is an equivalence relation on a set (A) and ([a]\cap[b]\neq \varnothing), which conclusion is definitely true?

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Class 12 · Mathematics

On all students, (xRy) if and only if (x) and (y) study in the same class. What will be the equivalence classes of this relation?

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Class 12 · Mathematics

On a set with (5) elements, exactly (2) equivalence classes are required. Which option gives possible class sizes?

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Class 12 · Mathematics

A partition ({{a,c,d},{b}}) is given on (A={a,b,c,d}). Which pair will not belong to the equivalence relation formed from it?

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Class 12 · Mathematics

If an equivalence relation has classes ({1,2}), ({3,4,5}), and ({6}), which statement about ((2,5)) and ((4,3)) is correct?

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Class 12 · Mathematics

For the relation (aRb) if and only if (a=b) or (a+b=6) on (A={1,2,3,4,5}), which is the correct partition?

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Class 12 · Mathematics

On (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). Is this an equivalence relation?

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Class 12 · Mathematics

On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) leave the same remainder on division by (2). What is the quotient set (A/R)?

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Class 12 · Mathematics

On (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a) and (b) are of the same type: both less than (4) or both greater than or equal to (4). How many ordered pairs are there?

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Class 12 · Mathematics

On (A={1,2,3,4,5}), the relation is (R={(a,b):a\equiv b \pmod{2}}). How many ordered pairs are in this relation?

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Class 12 · Mathematics

On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) are both multiples of (3) or both not multiples of (3). What is the equivalence class of (3)?

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Class 12 · Mathematics

If (A) has (5) elements and the partition of an equivalence relation is ({{a,b},{c,d,e}}), how many ordered pairs are in the relation?

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Class 12 · Mathematics

On the set of lowercase English alphabet letters, (aRb) if and only if (a) and (b) are both vowels or both consonants. How many equivalence classes does this relation form?

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Partition

If R is an equivalence relation on a set A, which statement about its equivalence classes is correct?

On (A={1,2,3,4,5,6}), relation (R) has classes ({1,6}), ({2,3,5}), and ({4}). Which pair definitely will not be in (R)?

On (A={1,2,3,4,5,6,7,8}), (aRb) if (a) and (b) lie in the same block among ({1,2}), ({3,4,5}), ({6,7,8}). How many pairs are in the relation?

If two equivalence classes ([a]) and ([b]) of an equivalence relation are distinct, what is true about their intersection?

On (A={1,2,3,4,5}), one equivalence class of (R) is ({1,2,5}). If (R) is an equivalence relation, which pair cannot be in (R)?

On (A={1,2,3,4}), the equivalence classes are ({1,4}) and ({2,3}). Which pair must belong to the relation?

A partition of (A={1,2,3,4,5}) is ({{1,3,5},{2,4}}). How many ordered pairs will be in the equivalence relation formed by this partition?

If (R) is an equivalence relation on a set (A) and ([a]\cap[b]\neq \varnothing), which conclusion is definitely true?

On all students, (xRy) if and only if (x) and (y) study in the same class. What will be the equivalence classes of this relation?

On a set with (5) elements, exactly (2) equivalence classes are required. Which option gives possible class sizes?

A partition ({{a,c,d},{b}}) is given on (A={a,b,c,d}). Which pair will not belong to the equivalence relation formed from it?

If an equivalence relation has classes ({1,2}), ({3,4,5}), and ({6}), which statement about ((2,5)) and ((4,3)) is correct?

For the relation (aRb) if and only if (a=b) or (a+b=6) on (A={1,2,3,4,5}), which is the correct partition?

On (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). Is this an equivalence relation?

On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) leave the same remainder on division by (2). What is the quotient set (A/R)?

On (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a) and (b) are of the same type: both less than (4) or both greater than or equal to (4). How many ordered pairs are there?

On (A={1,2,3,4,5}), the relation is (R={(a,b):a\equiv b \pmod{2}}). How many ordered pairs are in this relation?

On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) are both multiples of (3) or both not multiples of (3). What is the equivalence class of (3)?

If (A) has (5) elements and the partition of an equivalence relation is ({{a,b},{c,d,e}}), how many ordered pairs are in the relation?

On the set of lowercase English alphabet letters, (aRb) if and only if (a) and (b) are both vowels or both consonants. How many equivalence classes does this relation form?

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