Mathematics
Reflexive relation
Practice questions
If (A) is non-empty and (R) is reflexive on (A), which statement about (A\times A-R) is correct?If (R) is reflexive on (A), what can certainly be said about (R^{-1}\cap R)?If (R) and (S) are both reflexive relations on (A), what is the main reason that (S\circ R) is reflexive?On (A={1,2,3,4}), (R) is reflexive and symmetric and has 12 total pairs. How many such relations are possible?On (A={1,2,3,4,5,6,7,8}), (R={(a,b):a\equiv b \pmod{4}}). How many total pairs will (R) have?On (A={0,1,2,3,4,5}), (R={(a,b):a^2\equiv b^2 \pmod{6}}). How many total pairs are in (R)?For A={0,1,2,3,4,5} and R={(a,b): a²≡b² (mod 6)}, how many equivalence classes does R have?On the power set of (S={1,2,3,4}), (XRY) when (X\subseteq Y). How many reflexive pairs are in this relation?On the power set of (S={1,2,3,4}), (XRY) when (X\subseteq Y). How many total pairs will this relation have?On (A={2,4,6,8}), (R={(a,b):a+b\le k}). What is the minimum value of (k) for (R) to be reflexive?On (A={-2,-1,0,1,2}), (R={(a,b):a^2+b^2<k}). What is the minimum integer value of (k) for (R) to be reflexive?On (A={1,2,4,8,16}), (R={(a,b):a) is a divisor of (b)(}). How many total pairs will (R) have?On (A={-4,-2,0,2,4}), (R={(a,b):|a|=|b|}). How many non-self pairs are in (R)?If (R) is reflexive on (A) and (I_A) is the identity relation, what is correct about (R\cup I_A)?If (R) is reflexive on (A) and (I_A) is the identity relation, what is correct about (R\cap I_A)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,3)}). Which pair must appear in (R\circ R)?On (A={1,2,3,4}), (R) is reflexive and has exactly 7 pairs. How many such relations are possible?If (A) has (n) elements, what is the number of reflexive relations having exactly (n+3) pairs?On (A={1,2,3}), how many reflexive relations satisfy that if ((1,2)) is present then ((2,1)) is absent?If (R) is reflexive on (A), which statement about (R\cup R^{-1}) is always true?