• 072920 77839
  • info@smartachievers.in
Menu
Back
  • JEE ADVANCE
  • JEE MAIN
  • NEET
  • BITSAT
  • CBSE BOARD
  • UP BOARD
  • CUET
JEE ADVANCE
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
JEE MAIN
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
NEET
  • CLASS XI - XII
  • CRASH COURSE
BITSAT
  • CLASS XI - XII
CBSE BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
  • CLASS VI
  • CLASS VII
  • CLASS VIII
UP BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
CUET
  • CRASH COURSE
Courses


Solution


Q.

The number of relation on the set A = {1, 2, 3}, containing at most 6 elements including (1, 2), which are reflexive and transitive but not symmetric, is __________.          [2025]

Ans.

(5)

Given, A = {1, 2, 3}

Let the relation be R on A, which is reflexive and transitive but not symmetric, then

(1, 1), (2, 2), (3, 3), (1, 2) ∈ R

Remaining elements are

(2, 1), (2, 3), (1, 3), (3, 1), (3, 2)

Case I : If relation contains exactly 4 elements ⇒ 1 way

Case II : If relation contains exactly 5 elements, so we can add (1, 3) or (3, 2) ⇒ 2 ways

Case III : If relation contains exactly 6 elements, so we can add (2, 3), (1, 3) or (1, 3), (3, 2) or (3, 1), (3, 2) ⇒ 3 ways

∴   Total number of relations is 6.