Test on Equivalence relation

R is a relation on the set Z of integers and it is given by (x,y)  $\epsilon$  R  $\Longleftrightarrow$   $\left|x\ -\ y\right|\ \le1$  

• reflexive and transitive

• reflexive and symmetric

• symmetric and transitive

• an equivalence relation

If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is

• {1, 4, 6, 9}

• {4, 6, 9}

• {1}

• none of these

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y  $\Longleftrightarrow$  x is relatively prime to y. Then, domain of R is

• {2, 3, 5}

•  {3, 5}

• {2, 3, 4}

• {2, 3, 4, 5}

Let R be a relation on N defined by x + 2y = 8. The domain of R is

• {2, 4, 8}

• {2, 4, 6, 8}

• {2, 4, 6}

• {1, 2, 3, 4}

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3. Then, R is

• {(8, 11), (10, 13)}

• {(11, 8), (13, 10)}

• {(10, 13), (8, 11), (8, 10)}

• none of these

Let R = {(a, a), (b, b), (b, a), (a, b)} be a relation on set A = {a, b, c}. Then, R is

• identity relation

• reflexive

• symmetric

• equivalence

Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is

• neither reflexive nor transitive

• neither symmetric nor transitive

• transitive

• none of these

If R is the largest equivalence relation on a set A and S is any relation on A, then

• R $\subset$ S

• S $\subset$ R

• R = S

• none of these

If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y y = 3x, then R =

• {(3, 1), (6, 2), (8, 2), (9, 3)}

• {(3, 1), (6, 2), (9, 3)}

• {(3, 1), (2, 6), (3, 9)}

• none of these

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

If A = {a, b, c, d} then a relation R = {(a, b), (b, a), (a, a)} on A is

• symmetric and transitive only

• reflexive and transitive only

• symmetric only

• transitive only