Answer to Question #127927 in Discrete Mathematics for jaya

Question

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

Answer 1

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

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

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

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

The ordered pairs produced by the partitioned

Is then the collect of the all ordered pairs produced by one of the subsets

{(a,a),(a,b),(b,a)(b,b)

(c,c),(c,d),(d,c),(d,d)

(e,e),(e,f),(e,g),(f,e),(f,f),(f,g),(g,e),(g,f),(g,g)}

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

{a}=(a,a)

{b}=(b,b)

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

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

{g}=(g,g)

The ordered pairs produced by the partitioned

Is then the collect of the all ordered pairs produced by one of the subsets

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

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

The ordered pairs produced by the partitioned

Is then the collect of the all ordered pairs produced by one of the subsets

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

(e,e),(e,f),(e,g),(f,e),(f,f),(f,g),(g,e),(g,f),(g,g)}

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

{a,c,e,g}=(a,a),(a,c),(a,e),(a,g),(c,a),(c,c),(c,e),(c,g),(e,a),(e,c),(e,e),(e,g),(g,a),(g,c),(g,e),(g,g)

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

{f}=(f,f)

The ordered pairs produced by the partitioned

Is then the collect of the all ordered pairs produced by one of the subsets

{(a,a),(a,c),(a,e),(a,g),(c,a),(c,c),(c,e),(c,g),(e,a),(e,c),(e,e),(e,g),(g,a),(g,c),(g,e),(g,g)

(b,b),(b,d),(d,b),(d,d)

(f,f)}