Tugas Wahyuning trisnani

EXERCISE I :

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 :

Exercises 34–37 deal with these relations on the set of real numbers:

R1 = {(a, b) ∈ R2 | a>b}, the “greater than” relation,

R2 = {(a, b) ∈ R2 | a ≥ b}, the “greater than or equal to”relation,

R3 = {(a, b) ∈ R2 | a<b}, the “less than” relation,

R4 = {(a, b) ∈ R2 | a ≤ b}, the “less than or equal to”relation,

R5 = {(a, b) ∈ R2 | a = b}, the “equal to” relation,

R6 = {(a, b) ∈ R2 | a=b}, the “unequal to” relation.

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

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.

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 :

EXERCISE II :

Answer :

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