Relation and Function-Discrete Math

what is equivalence relation

• reflexive, antisymmetric, transitive

• reflexive, symmetric, transitive

• reflexive, asymmetric, transitive

• reflexive, antisymmetric, symmetric

Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø Then (pick the TRUE statement)

• R is relexive and transitive

• R is an equivalence relation

• R is symmetric and not transitive

• R is not relexive and not symmetric

A relation R is defined on the set of positive integers as xRy if 2x + y ≤ 5. The realation R is

• reflexive

• transitive

• symmetric

• none

The universal relation A x A on A is

• anti-symmetric

• an equivalence relation

• a partial ordering relation

• not symmetric and not anti-symmetric

Let R be a relation on N given by R={(x,y):x=y-2, y>6}, then

• (2,4)∈R

• (3,8)∈R

• (8,7)∈R

• (6,8)∈R

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

If A={a,b,c} theen R={(b,c)}, then R is

• Reflexive only

• Symmetric only

• Transitive only

• equivalence relation

Let A={1,2,3}, and R is {(1,1),(1,2),(1,3), (2,2), (2,3), (3,3)}, then R is

• reflexive but not symmetric

• reflexive but not transitive

• symmetric and transitive

• neither symmetric nor transitive

For real numbers x and y define xRy iff x-y+√2 is an irrational number. then R is

• reflexive

• symmetric

• transitive

• none of these

Tags

CCSS.HSN.RN.B.3

the maximum number of equivalence relation in set A={1,2,3} is

• 1

• 2

• 4

• 5

Tags

CCSS.HSS.CP.B.9

The domain of R={(x,y): x²+y²≤4, x,y∈ Z}

• {0,1.2}

• {0,-1,-2}

• {1,2}

• none of these

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.10

CCSS.HSG.GPE.A.1