Mathematics
Symmetric relation
Practice questions
If (R=R^{-1}), what can be said about (R)?On (A={1,2,3,4}), (R={(a,b):a<b}). Why is (R) not symmetric?On A={1,2,3}, R={(1,1),(2,2),(3,3),(1,2),(2,1)}. Which statement is correct?On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). Which statement is correct?If (R) and (S) are both symmetric relations on (A), what is true about (R\cap S)?If (R) and (S) are both symmetric relations on (A), which statement is true about (R\cup S)?If (R) is symmetric, which statement is always true about (R\setminus S)?On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). Will ((1,3)) belong to (R\circ R)?For every symmetric relation (R), will (R\circ R) also be symmetric?On A={1,2,3,4}, R={(a,b): |a-b|=1}. What type is R?On (A={1,2,3,4}), (R={(a,b):a\text{ divides }b}). Is (R) symmetric?On real numbers, the relation (R={(a,b):a^2=b^2}) is given. Choose the correct statement about (R).On integers, (R={(a,b):a+b\equiv 0 \pmod{3}}). Which statement is correct for (R)?On integers, (R={(a,b):a-b\equiv 1 \pmod{4}}). Is (R) symmetric?On integers, (R={(a,b):a-b\equiv 0 \pmod{5}}). Why is (R) symmetric?Which relation needs at least one pair to be added to make it symmetric?How many pairs will be in the smallest symmetric relation containing (R={(1,2),(2,3),(3,1)})?What is the symmetric closure of (R={(1,1),(1,2),(2,1),(2,3)})?Why is the empty relation ∅ considered symmetric on any set A?Why is the universal relation (A\times A) symmetric on a set (A)?