Mathematics
Reflexive relation
Practice questions
If (A={1,2,3,4}) and (P={(1,2),(2,1),(4,4)}), how many reflexive relations (R) on (A) satisfy (P\subseteq R)?If (A) has 5 elements, what is the number of reflexive relations on (A) having exactly 8 pairs?On (A={1,2,3}), how many reflexive relations are neither the identity relation nor the universal relation?On (A={1,2,3,4}), how many reflexive relations have at least 6 pairs?On (A={1,2,3}), how many reflexive relations contain exactly one of the pairs ((1,2)) and ((2,1))?If (R) is reflexive on (A) and (S\subseteq A\times A) has no self-pair, which statement about (R-S) is correct?If (A) is non-empty and (R) is reflexive on (A), what is the correct conclusion about (A\times A-R)?If (R) is reflexive on (A), what is the correct reason that (R^{-1}) is reflexive?If (R) and (S) are both reflexive on (A), which middle element works to show (S\circ R) is reflexive?On (A={1,2,3}), (R) is reflexive and symmetric and has total 7 pairs. How many such relations are possible?On (A={1,2,3,4}), (R) is reflexive and symmetric and has total 8 pairs. How many such relations are possible?On (A={1,2,3,4,5,6}), (R={(a,b):a\equiv b \pmod{3}}). How many total pairs will (R) have?On (A={0,1,2,3,4}), (R={(a,b):a^2\equiv b^2 \pmod{5}}). How many total pairs are in (R)?On (A={-3,-2,-1,0,1,2,3}), (R={(a,b):|a|=|b|}). How many total pairs will (R) have?On (A={1,2,3,4,6,12}), (R={(a,b):a) is a divisor of (b)(}). How many total pairs will (R) have?On the power set of (S={1,2,3}), (XRY) when (X\subseteq Y). How many total pairs will this relation have?On the power set of (S={1,2,3}), (XRY) when (X\subset Y). How many pairs must be added to make (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\le k}). What is the minimum value of (k) for (R) to be reflexive?On (A={1,3,5}), (R={(a,b):a+b<k}). What is the minimum integer value of (k) for (R) to be reflexive?On (A={2,4,6}), (R={(a,b):|a-b|<k}). Which condition on (k) is necessary and sufficient for (R) to be reflexive?