Mathematics
Reflexive relation
Practice questions
On (A={1,2,3,4}), (R={(a,b):a \equiv 0 \pmod{2}}). Why is this relation not reflexive?On natural numbers, relation (R) is defined by ((a,b)\in R) when (a) divides (b). Which statement is correct for (R)?On natural numbers, (R={(a,b):a) is a proper divisor of (b)(}), where proper divisor means (a\ne b). What is (R)?On the family of all subsets of (S={1,2,3}), (R) is defined by (XRY) when (X\subseteq Y). Is (R) reflexive?On a family of sets, (R) is defined by (XRY) when (X\subset Y). Why is this relation not reflexive?On real numbers, (R={(a,b):|a-b|\le 0}). What is the correct conclusion about (R)?On real numbers, (R={(a,b):|a-b|>0}). Why is (R) not reflexive?On (A={1,2,3,4}), (R={(a,b):a+b) is even(}). (R) is reflexive because which statement is true?On (A={1,2,3,4}), (R={(a,b):a+b) is odd(}). What type of pairs must be added to make it reflexive?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}) and (S={(1,1),(2,2),(3,3),(2,3)}). What is correct about (R\cap S)?If (R) and (S) are both reflexive relations on (A), which statement about (R\cup S) is correct?If (R) and (S) are both reflexive relations on (A), which statement about (R-S) is generally correct?If (R) is reflexive on (A) and (R\subseteq T\subseteq A\times A), what conclusion follows about (T)?If (T\subseteq R) and (R) is reflexive on (A), which statement is correct for (T)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3)}). If any one extra pair from (A\times A) is added to (R), what will the new relation be?On (A={1,2,3,4}), what type of relation is formed if ((3,3)) is removed from the identity relation?On (A={1,2,3}), (R=A\times A-{(2,2)}). Which statement about (R) is correct?On (A={1,2,3}), (R=A\times A-{(1,2),(2,3)}). What is (R)?On (A={1,2,3,4}), what is the difference between the number of pairs in the minimum reflexive relation and the universal relation?A set (A) has 5 elements. What is the ratio of the number of all relations to the number of reflexive relations on (A)?