Mathematics
Reflexive relation
Practice questions
On (A={1,2,3}), (R={(a,b):|a-b|>0}) is given. What is (R)?On the empty set (A=\varnothing), the empty relation (R=\varnothing) is given. Which statement about reflexivity is correct?On a non-empty set (A), the empty relation (R=\varnothing) is given. Which statement about (R) is correct?For any set (A), what is correct about the universal relation (A \times A)?If (A) is non-empty and (R) is a reflexive relation on (A), what is correct about (A \times A-R)?If (R) is a reflexive relation on (A) and (S) is any relation on (A), which statement about (R \cup S) is correct?If (R) and (S) are reflexive relations on (A), which statement about (S \circ R) is correct?If (R) is reflexive on (A) and (B \subseteq A), on which set is (R \cap (B \times B)) reflexive?If (R) is reflexive on (A) and (S \subseteq R), which statement about (S) is always true?What is the smallest reflexive relation on a set (A)?On (A={1,2,3}), how many reflexive relations must contain both ((1,2)) and ((2,3))?How many relations on a four-element set are both reflexive and symmetric?How many relations on a three-element set are both reflexive and antisymmetric?Which matrix of a relation on a three-element set makes the relation reflexive?The matrix of a relation is (\begin{bmatrix}1&1&0\0&1&1\1&0&1\end{bmatrix}). Which statement about the relation is correct?If a relation matrix has all off-diagonal entries (1), but one main diagonal entry is (0), what is the relation like?Which statement about equivalence relations and reflexive relations is correct?If (f:A \to B) is a function and (R={(x,y):f(x)=f(y)}) on (A), which statement about (R) is correct?If (f:A \to \mathbb{R}) and (R={(x,y):f(x)<f(y)}), what is correct about (R)?If (f:A \to \mathbb{R}) and (R={(x,y):f(x)\le f(y)}), what is (R)?