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# Relations Worksheet

Relations Worksheet
• 1. If there are three relations R1, R2, R3 are defined on set S = p, q, r as follows.
R1 = (p, p), (p, q), (p, r), (q, q), (q, r), (r, p), (r, q), (r, r);
R2 = (p, q), (q, p), (p, r), (r, p),
R3 = (p, q), (q, r), (r, p) then show that the relations R1, R2, R3 are?
1. Reflexive, symmetric and transitive
2. Reflexive, not symmetric and transitive
3. Not reflexive but symmetric and transitive
4. None
• 2. Show that the relation ‘R’ on set ‘S’ = 3, 4, 5 is given by R = (3, 3), (4, 4), (5, 5), (3, 4), (4, 5) then the relation is?
1. Reflexive, symmetric and transitive
2. Reflexive but neither symmetric nor transitive
3. Not reflexive but symmetric and transitive
4. None
• 3. If there are three relations R1, R2, R3 are defined on set S = 2, 3, 4 as follows.
R1 = (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4),
R2 = (2, 3), (3, 2), (2, 4), (4, 2),
R3 = (2, 3), (3, 4), (4, 2) then show that the given relation is?
1. Reflexive, symmetric and transitive
2. Reflexive but neither symmetric nor transitive
3. Not reflexive but symmetric and transitive
4. None
• 4. The relation R on R defined as R = (x, y): x ≤ y, then show that the relation is?
1. Reflexive, symmetric and transitive
2. Reflexive but neither symmetric nor transitive
3. Reflexive and transitive but not symmetric
4. None
• 5. If there are three relations R1, R2 are defined on set P = u, v, w as follows.
R1 = (u, u, (u v), (u, w), (v, v), (v, w), (w, u), (w, v), (w, w);
R2 = (u, v), (v, u), (u, w), (w, u),
Then show that the relation R1, R2 is?
1. Reflexive, symmetric and transitive
2. Reflexive, not symmetric and transitive
3. Not reflexive but symmetric and transitive
4. None
• 6. Show that the relation ‘R’ on set S = 6, 7, 8 is given by R = (6, 6), (7, 7), (8, 8), (6, 7), (7, 8) then show the relation is?
1. Reflexive, symmetric and transitive
2. Reflexive but neither symmetric nor transitive
3. Not reflexive but symmetric and transitive
4. None
• 7. If there are three relations R1, R2 are defined on set S = x, y, z as follows.
R1 = (x, x), (x, y), (x, z), (y, y), (y, z), (z, x), (z, y), (z, z),
R2 = (x, y), (y, z), (x, z), (z, x), then show that the relation is?
1. Reflexive, symmetric and transitive
2. Reflexive but neither symmetric nor transitive
3. Not reflexive but symmetric and transitive
4. None
• 8. The relation R on R defined as R = (a, b): a ≥ b, then show that the relation is?
1. Reflexive, symmetric and transitive
2. Reflexive but neither symmetric nor transitive
3. Reflexive and transitive but not symmetric
4. None
• 9. Show that the relation R on the set R of all the real numbers, defined as R = (x, y): x ≤ y2 then show that the relation R is?
1. Reflexive, symmetric and transitive
2. Neither reflexive nor symmetric nor transitive
3. Reflexive and transitive but not symmetric
4. None
• 10. Show that the relation R on the set R of all the real numbers, defined as R = (x, y): x2 ≤ y then show that the relation R is?
1. Reflexive, symmetric and transitive
2. Neither reflexive nor symmetric nor transitive
3. Reflexive and transitive but not symmetric
4. None
Math Topics