Question

Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is
R1 ∪ R2 also symmetric?

Accepted Answer

Let  R_1  and  R_2  be symmetric relations. Let us prove that  R_1 u2229 R_2  is also symmetric. Let  (a,b) in R_1 cap R_2.  Then  (a,b) in R_1  and  (a,b) in R_2.   Since  R_1  and  R_2  are symmetric relations,  (b,a) in R_1  and  (b,a) in R_2.  It follows that  (b,a) in R_1 cap R_2,  and hence  R_1 u2229 R_2  is also symmetric relation.

Question #284575

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