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Class 12 · Mathematics · Easy

On (A={1,2,3}), (R={(1,2),(2,1),(2,3)}). Why is (R) not symmetric?

Class 12 · Mathematics · Easy

If (R={(2,2),(3,5),(5,3)}), which statement about (R) is correct?

Class 12 · Mathematics · Easy

On the set (A={1,2,3}), which relation is not symmetric?

Class 12 · Mathematics · Easy

Which statement correctly identifies a symmetric relation?

Class 12 · Mathematics · Easy

On (A={1,2}), (R={(1,1),(1,2)}) is given. Which pair must be added to make it symmetric?

Class 12 · Mathematics · Easy

If a relation (R) contains ((4,7)) and (R) is symmetric, which ordered pair must definitely be in (R)?

Class 12 · Mathematics · Easy

On the set (A={1,2,3}), the relation (R={(1,2),(2,1),(3,3)}) is given. What type of relation is it?

Class 12 · Mathematics · Expert

How many reflexive relations are possible on a set with six elements?

Class 12 · Mathematics · Expert

If (A={1,2,3,4,5,6}) and (R={(a,b):a^2+b^2\text{ is divisible by }10}), how many diagonal pairs are already in (R)?

Class 12 · Mathematics · Expert

On (A={1,2,3,4,5}), (R={(a,b):a+1\mid b+1}). Is (R) reflexive?

Class 12 · Mathematics · Expert

On (A={0,1,2,3,4}), (R={(a,b):a^2\equiv b^2 \pmod{4}}). What is the correct reason for (R) being reflexive?

Class 12 · Mathematics · Expert

Let (A={1,2,3,4,5,6}) and (R={(a,b)\in A\times A:a+b\text{ is divisible by }4}). What is the minimum number of pairs required to make (R) reflexive?

Class 12 · Mathematics · Hard

If (R) is reflexive on (A), which statement about (R\cup R^{-1}) is always true?

Class 12 · Mathematics · Hard

If (R) is reflexive on (A) and (I_A) is the identity relation, what is correct about (R\cup I_A)?

Class 12 · Mathematics · Hard

On the power set of (S={1,2,3,4}), (XRY) when (X\subseteq Y). How many reflexive pairs are in this relation?

Class 12 · Mathematics · Hard

If (R) and (S) are both reflexive relations on (A), what is the main reason that (S\circ R) is reflexive?

Class 12 · Mathematics · Hard

On (A={1,2,3,4}), how many reflexive relations have at most 6 pairs?

Class 12 · Mathematics · Hard

If (A={1,2,3,4}) and (P={(1,3),(3,1),(2,2)}), how many reflexive relations (R) on (A) satisfy (P\subseteq R)?

Class 12 · Mathematics · Expert

On (A={1,2,3,4,5,6}), (R={(a,b):\operatorname{lcm}(a,b)=a}). Why is (R) reflexive?

Class 12 · Mathematics · Expert

If (A={1,2,3,4,5}) and (R={(a,b):\gcd(a,b)=a}), is (R) reflexive?