Mathematics
Symmetric relation
Practice questions
If (R) and (S) are both symmetric relations, what is true about (R\cap S)?If (R) and (S) are both symmetric relations, what is the correct statement about (R\cup S)?If (R) is symmetric, what can be said about the complement of (R) with respect to (A\times A)?On (A={1,2,3}), (R={(1,1),(2,2),(1,2),(2,1),(2,3),(3,2)}). Which property is definitely present?Which of the following statements is false?Why is the empty relation (\varnothing) on a non-empty set (A) considered symmetric?Why is the universal relation (A\times A) symmetric?Which statement is correct about the identity relation (I={(a,a):a\in A})?On (A={1,2,3,4,5}), (R={(a,b):a\equiv b \pmod{2}}). Choose the correct option about (R).Why is (R={(a,b):a\equiv b \pmod{3}}) symmetric on (A={1,2,3,4,5})?Which option gives a relation (R) that is symmetric but not reflexive?Which option gives a relation that is reflexive but not symmetric?If (R={(1,2),(2,1),(2,3),(3,2),(1,3)}), which pair must be added to make (R) symmetric?If a symmetric relation (R) on (A={1,2,3}) contains ((1,2)) and ((2,3)), which pairs must also be present at minimum?On (A={1,2,3}), (R={(a,b):ab\text{ is even}}). Is (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a+b=5}). What is (R)?On (A={1,2,3,4}), (R={(a,b):a-b=2}). Why is (R) not symmetric?In which relation is it not necessary that ((b,a)\in R) whenever ((a,b)\in R)?If (R) is a symmetric relation and ((2,5),(5,7)\in R), which option is definitely true?If a relation (R) is symmetric, which conclusion is not necessary?