DISCRETE MATH CHAPTER 3

PROPERTIES OF RELATIONS

REFLEXIVE

▪ A relation R is ________ if for every a ∈ A, (a, a) ∈ R

should be:

• element a is part of set A

• kumpleto sa relation yung ordered pair

• if set a is 1,2,3 then sa relation ay dapat (1,1) (2,2) (3,3)

SYMMETRIC

• A relation R is _______ if whenever (a, b) ∈ R, then (b, a) ∈ R.

• if existing yung ordered pair na a and b, pag binaliktad mo sya dapat nandyon parin sya
  

  ex: 1,1 pag binaliktad 1,1 paren

• A relation is not _______ if there exists (a, b) ∈ R but (b, a) ∉ R.

  should be:

• if existing yung ordered pair na a and b, pag binaliktad mo sya dapat nandyon parin sya, pero if may isang hindi nagkapareho, then it is not.

  ex: 1,1 , at 1,3 then not sya

ANTISYMMETRIC

• A relation R is __________if whenever (a, b) and (b, a) belong to R then a = b.

EX: (a,b)(b,a) substitute (1,1)(1,1)

dapat yung value ng domain ay equal sa domain ng 2nd pair, also yung value ng range ay dapat equal sa range value ng 2nd pair

• A relation R is not ________ if there exists (a, b) ∈ A such that (a, b) and (b, a) belong to R but a ≠ b.
  

TRANSITIVE

• A relation R on a set A is ________ if whenever (a, b), (b, c) ∈

  R then (a, c) ∈ R.

yung range (b) ng 1st pair ay dapat same value ng domain (a) ng other pair then also dapat mayroong domain (a) ng 1st pair and range (b) ng other pair sa relations

it doesn’t matter kung magkalayo yung pair, as long as mayroong match na range and domain, at mayroong relations na domain and range

dapat ang tatlong ito ay makita sa relations

ex: (1,2),(2,3) then (1,3)

• A relation R is not ________ if there exists (a, b, c) ∈ A such that (a, b), (b, c) ∈ R, but (a, c) ∉ R.