• 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.

Let A = {1, 2, 3,…,20}. Let R1 and R2 be two relation on A such that R1 = {(a, b) : b is divisible by a} R2 = {(a, b) : a is an integral multiple of b} Then, number of elements in R1-R2 is equal to _______ .                [2024]

Ans.

(46)

R1= {(1, 1), (1, 2)…(1, 20), (2, 2), (2, 4),…(2, 20), (3, 3), (3, 6)…(3, 18), (4, 4), (4, 8),…(4, 20), (5, 5), (5, 10), (5, 15), (5, 20), (6, 6), (6, 12), (6, 18), (7, 7), (7, 14), (8, 8), (8, 16), (9, 9), (9, 18), (10, 10), (10, 20), (11, 11), (12, 12), (13, 13), (14, 14), (15, 15), (16, 16), (17, 17), (18, 18), (19, 19), (20, 20)}

R2= {(20, 1), (20, 2), (20, 4), (20, 5), (20, 10), (20, 20), (19, 19), (19, 1), (18, 1), (18, 2), (18, 3), (18, 6), (18, 9), (18, 18), (17, 1), (17, 17), (16, 1), (16, 2), (16, 4), (16, 8), (16, 16), (15, 1), (15, 3), (15, 5), (15, 15), (14, 1), (14, 2), (14, 7), (14, 14), (13, 1), (13, 13), (12, 1), (12, 2), (12, 3), (12, 4), (12, 6), (12, 12), (11, 1), (11, 11), (10, 1), (10, 2), (10, 5), (10, 10), (9, 1), (9, 3), (9, 9), (8, 1), (8, 2), (8, 4), (8, 8), (7, 1), (7, 7), (6, 1), (6, 2), (6, 3), (6, 6), (5, 1), (5, 5), (4, 1), (4, 2), (4, 4), (3, 1), (3, 3), (2, 1), (2, 2), (1, 1)}

R1∩R2 = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8), (9, 9), (10, 10), (11, 11), (12, 12), (13, 13), (14, 14), (15, 15), (16, 16), (17, 17), (18, 18), (19, 19), (20, 20)}

Number of elements in R1-R2=66-20=46 elements.