Mathematics
Reflexive relation
Practice questions
If (A) has (5) elements, what is the difference between the number of pairs in the smallest reflexive relation and the universal relation?On (A={1,2,3}), (R) is reflexive. If (R) has (5) pairs in total, how many extra pairs are there besides self-pairs?On (A={1,2,3,4}), (R) is not reflexive. Still, what is the maximum possible number of pairs in (R)?On (A={1,2,3}), (R={(a,b):|a-b|\ge 0}). Choose the correct answer about (R).On (A={1,2,3}), (R={(a,b):|a-b|>0}). Why is (R) not reflexive?On (A={1,2,3}), (R={(a,b):a) and (b) have the same parity(}). Is (R) reflexive or not?On (A={1,2,3,4}), (R={(a,b):a\equiv b \pmod{3}}). Which statement is sufficient to show that (R) is reflexive?On (A={1,2,3}), (R={(a,b):a+b\text{ is divisible by }2}) and (S={(a,b):a=b}). Which statement is correct?If (R) is reflexive on (A), what can be said about (I_A\subseteq R)?On (A={1,2,3}), (R) is reflexive and (R\subseteq S\subseteq A\times A). What is correct about (S)?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). If (T=R\setminus{(2,2)}), what will (T) be?On (A={1,2,3,4}), (R={(a,b):a-b\text{ is divisible by }4}). Is (R) reflexive?On (A={1,2,3}), (R={(a,b):a^2+b^2=2ab}). Which statement is correct about (R)?On (A={1,2,3}), (R={(a,b):(a-b)^2=0}). How should (R) be identified?On (A={1,2,3}), (R={(a,b):a^2-b^2=0}). Why is (R) reflexive?On (A={1,2,3,4}), (R={(a,b):a) and (b) are both even or both odd(}). Choose the correct statement for (R).On (A={1,2,3}), (R={(a,b):a+b\le 5}). Is (R) reflexive or not?On (A={1,2}), (R={(1,1),(2,2),(1,2)}). What is correct about the complement relation (R^c)?If (R=A\times A) and (A) is non-empty, which statement about (R^c) is correct?On (A={1,2,3}), (R={(a,b):a) and (b) leave the same remainder when divided by (2)(}). Which pair will definitely be in (R)?