Matematika Diskrit

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3. For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} c) {(2, 4), (4, 2)} d) {(1, 2), (2, 3), (3, 4)} e) {(1, 1), (2, 2), (3, 3), (4, 4)} f ) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} Answer : 34. Find a) R1 ∪ R3. b) R1 ∪ R5. c) R2 ∩ R4. d) R3 ∩ R5. e) R1 − R2. f ) R2 − R1. g) R1 ⊕ R3. h) R2 ⊕ R4 Answer : 35. Find a) R2 ∪ R4. b) R3 ∪ R6. c) R3 ∩ R6. d) R4 ∩ R6. e) R3 − R6. f ) R6 − R3. g) R2 ⊕ R6. h) R3 ⊕ R5 Answer : 36. Find a) R1 ◦ R1. b) R1 ◦ R2. c) R1 ◦ R3. d) R1 ◦ R4. e) R1 ◦ R5. f ) R1 ◦ R6. g) R2 ◦ R3. h) R3 ◦ R3. Answer : 37. Find a) R2 ◦ R1. b) R2 ◦ R2. c) R3 ◦ R5. d) R4 ◦ R1. e) R5 ◦ R3. f ) R3 ◦ R6. g) R4 ◦ R6. h) R6 ◦ R6. Answer : ...