Solution for Section 10.2 Question 1

1.  R₁ = { (1,1), (1,2), (2,1), (2,2), (3,4), (4,1), (4,4) } is:

• not reflexive since it does not contain the ordered pair (3, 3);
• not symmetric since it contains the ordered pair (3, 4) but not the ordered pair (4, 3);
• not transitive since it contains the ordered pairs (3, 4) and (4, 1) but not the ordered pair (3, 1).

R₂ = { (1,1), (1,2), (2,1), (2,2), (3,3), (4,4) } is :

• reflexive;
• symmetric;
• transitive.

R₃ = { (1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1), (4,4)} is :

• reflexive;
• symmetric;
• not transitive since it contains the ordered pairs (2, 1) and (1, 4) but not the ordered pair (2, 4).

R₄ = { (2,1), (3,1), (3,2), (4,1), (4,2), (4,3) } is :

• not reflexive since it does not contain the ordered pair (1, 1) or (2, 2) etc.;
• not symmetric since it contains the ordered pair (2, 1) but not the ordered pair (1, 2);
• transitive.

R₅ = { (1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4), (4,4)} is :

• reflexive;
• not symmetric since it contains the ordered pair (1, 2) but not the ordered pair (2, 1);
• transitive.

R₆ = { (1,1), (2,2), (3,3), (4,4) } is :

• reflexive;
• symmetric;
• transitive.

Back to Section 10.2