Assignment on Relations

Problems 1 to 7 each is 2 points. Problem 8 is 6 points.

Consider these relations,

1. R1 = { ( a, b) | a = 2b }

2. R2 = { (a, b) | a = b }

3. R3 = { ( a, b) | a <= b }

4. R4 = { (a, b) | a + b < 5 }

Which of the above mentioned relations contain the pairs ( 1, 1), ( 2, 1), ( 3, 1), (0, 1), (3, 3), (2, 2), (7, 2) , ( 6, 3), ( 3, 6), (2, 4)

Write the relation and the pairs under the relation

Consider this set A = { a, b, c, d } and the following relations

R6 = { ( a, a ), ( a, b), ( b, b), ( c, d ) }

R7 = { ( a, a), ( b, b ), ( b, c ), ( c, c ), ( c, d), (d, d) }

R8 = { (a, b), (a, d), ( b, a), ( d, a) , ( b, d) , (d, b) }

R9 = { ( a, a), ( b, c) }

R10 = { ( a, b), (b, d), (a, d), ( a, a ) , (b, b), (b, d) }

R11 = { (a, a), ( a, d) }

5. Which of the above relations are reflexive and state why ?

6. Which of the above relations are symmetric and state why ?

7. Which of the above relations are transitive and state why ?

8. Is below mentioned R12 a Equivalence relation ? and state why or why not ?

Consider this set S = { 1, 2 , 3}

R12 = { ( 1, 1), ( 1, 2 ), (2, 1) , (2 , 2 ), (3, 3), (1, 3) , (3, 1) }