raw the digraphs representing each of the relations.(a) R1 = {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)}(b) R2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}(c) R3 = {(2, 4), (3, 1), (3, 2), (3, 4)}
Question
raw the digraphs representing each of the relations.(a) R1 = {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)}(b) R2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}(c) R3 = {(2, 4), (3, 1), (3, 2), (3, 4)}
Solution
To draw the digraphs representing each of the relations, follow these steps:
(a) R1 = {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)}
Step 1: Draw four points and label them as a, b, c, and d. Step 2: Draw an arrow from a to a (since (a, a) is in the relation). Step 3: Draw an arrow from a to b (since (a, b) is in the relation). Step 4: Draw an arrow from b to c (since (b, c) is in the relation). Step 5: Draw an arrow from c to b (since (c, b) is in the relation). Step 6: Draw an arrow from c to d (since (c, d) is in the relation). Step 7: Draw an arrow from d to a (since (d, a) is in the relation). Step 8: Draw an arrow from d to b (since (d, b) is in the relation).
(b) R2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}
Step 1: Draw four points and label them as 1, 2, 3, and 4. Step 2: Draw arrows according to the pairs in the relation. For example, draw an arrow from 1 to 2 (since (1, 2) is in the relation), from 1 to 3, from 1 to 4, from 2 to 1, and
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