Question 367564
R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, 4)}
 
a) reflexive since for all element i, i<->i, i is in relation with itself
  (1,1), (2,2), (3,3), (4,4)
 
 symmetric, since if (a,b) exists, (b,a) exists too (1,2), (2,1); (1,4), (4,1)
 
 transitive, since the cases are trivial : (1,2)(2,2), (2,1)(1,1), (1,4)(4,4)
 
 
b) 

{{{drawing( 400, 300, -10, 10, -10, 10,

  circle(0, 0, 6),

  locate( -3, 2, "1" ),
  locate( 3, 2, "2" ), 
  locate( 2.6, -2, "3" ),
  locate( -2.6, -2, "4" ),
 
  line( -2.6, 1.5, 2.9, 1.5),

  triangle(-2.6, 1.5, -2.2, 1.8, -2.2, 1.1),
  triangle(2.9, 1.5, 2.5, 1.8, 2.5, 1.1),

  line( -2.8, 1.2, -2.8, -1.9),

  triangle(-2.8, 1.2, -2.3, .9, -3.1, .9),
  triangle(-2.8, -1.9, -2.5, -1.5, -3.1, -1.5),

  circle(-3.2, 2.6, 0.6),
  circle(3.8, 2.4, 0.6),
  circle(-3.8, -2.6, 0.6),
  circle(3.8, -2.8, 0.6),

  triangle(-2.6, 2.9, -2.9, 2.2, -2.3, 2.2),
  triangle(3.2, 2.1, 3.6, 2.8, 2.9, 2.8),
  triangle(-3.2, -2.1, -2.9, -2.7, -3.5, -2.7),
  triangle(3.2, -2.5, 3.6, -3.1, 2.9, -3.1)
  ) 
}}}
 
 
c) 

{{{(matrix(4,4,1, 1, 0, 1,
1, 1, 0, 0,
0, 0, 1, 0,
1, 0, 0, 1))
}}}