Mathematics
Symmetric relation
Practice questions
What is the total number of symmetric relations on (A={1,2,3,4,5})?If (A) has (4) elements, how many symmetric relations necessarily contain all diagonal pairs?If (A) has (4) elements, how many symmetric relations have no diagonal pair?If (R) and (S) are symmetric relations, which statement about the composition (R\circ S) is always true?On real numbers, (R={(a,b):a^2+b^2=1}). Which statement about (R) is correct?On real numbers, (R={(a,b):a^2-b^2=0}) is given. What type is this relation?If a relation contains ((2,5)) but does not contain ((5,2)), which conclusion is definite?On (A={1,2,3}), which relation is symmetric but not reflexive?On (A={1,2,3}), which relation is reflexive but not symmetric?Which is the most accurate definition of a symmetric relation?On the set (A={1,2,3}), the relation (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}) is given. Which minimum ordered pair must be added to make (R) symmetric?On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}) is defined. What type of relation is it?On the set of real numbers, relation (R) is defined by (aRb) if and only if (a-b>0). Is (R) symmetric?On (A={1,2,3,4,5}), (R={(a,b):|a-b|=2}). Choose the correct statement about (R).How many symmetric relations can be formed on A = {1, 2, 3}?A set (A) has (4) elements. How many symmetric relations are possible on (A)?On (A={1,2,3,4}), (R={(a,b):a\mid b}). Is (R) symmetric?On integers, relation (R) is defined by (aRb) if (a-b) is divisible by (5). Which statement is correct about (R)?On (A={1,2,3,4}), (R={(a,b):a+b=5}). Choose the correct statement about (R).On real numbers, (R={(a,b):a^2=b^2}). Why is this relation symmetric?