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Operations on the relations THE UNION R US

The union of the relations R and S on the same set A is defined in the following way:

(a, b) (ER U S <=Ąa, b) eR V(a, b) (ES or a{R U S)b <=>aRb VaSb.

THE INTERSECTION R D S

The intersection of the relations R and 5 on the same

set A is defined in the following way:

(a, b) (ER n S <=K.a, b) (ER A{a, b) (ES or a(R n S)b <=>tiRbAaSb.

Example:

Let R - relation of congruence modulo 3:

Vm, n ETA m =n(mod 3) <^31 (m ~ń).

Let 5 - relation of congruence modulo 5:

Vm, n (=Z m =n(mod 5) &5\(m ~>i).

Then:

m(R H S)n <-^31(jn~n) AS\{m ~n) /^15l(m-n) <=> m =n(mod 15).

m(R U S)n Ć23I (in~n) 1/51 (w ~n).

Relations on