List the ordered pairs in the equivalence relations produced by these partitions of {a, b, c, d, e, f, g}: a) {a, b},{c, d},{e, f, g} b) {a}, {b}, {c, d}, {e, f }, {g} c) {a, b, c, d},{e, f, g}

Question

Mathematics

Julianna Ayala

14 October, 14:59

List the ordered pairs in the equivalence relations produced by these partitions of {a, b, c, d, e, f, g}: a) {a, b},{c, d},{e, f, g} b) {a}, {b}, {c, d}, {e, f }, {g} c) {a, b, c, d},{e, f, g}

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Answers (1)

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Felix Bradshaw · Answer 1

a) {a, b}, {c, d}, {e, f, g},{a, b } = { (a, a) (b, b) (a, b) (b, a) },{c, d } = { (c, c) (d, d) (c, d) (d, c) },{e, f, g} = { (e, e) (e, f) (f, e) (e, g) (f, f) (f, g) (g, e) (g, f) (g, g) }

b) { (a, a) (b, b) (c, c) (c, d) (d, c) (d, d) (e, e) (e, f) (f, e) (f, f) (g, g)

c) { (a, a) (a, b) (b, b) (b, a) (a, c) (c, a) (b, c) (c, b) (c, c) (d, a) (a, d) (b, d) (d, b) (d, c) (c, d) (d, d) (c, c) (c, f) (f, c) (f, f) (c, g) (g, c) (f, g) (g, f) (g, g)

Step-by-step explanation:

a) {a, b}, {c, d}, {e, f, g}

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

{c, d } = { (c, c) (d, d) (c, d) (d, c) }

{e, f, g} = { (e, e) (e, f) (f, e) (e, g) (f, f) (f, g) (g, e) (g, f) (g, g) }

b) {a},{b},{c, d},{e, f},{g}

{ (a, a) (b, b) (c, c) (c, d) (d, c) (d, d) (e, e) (e, f) (f, e) (f, f) (g, g) }

c) {a, b, c, d},{e, f, g}

{ (a, a) (a, b) (b, b) (b, a) (a, c) (c, a) (b, c) (c, b) (c, c) (d, a) (a, d) (b, d) (d, b) (d, c) (c, d) (d, d) (c, c) (c, f) (f, c) (f, f) (c, g) (g, c) (f, g) (g, f) (g, g)