Discrete Math - Test 1

Front 1

Let R1 and R2 be relations on a set A. If R1 and R2 satisfy a given
property from the list of six, does R1 ∩ R2 also satisfy that property?

Back 1

Yes

Front 2

Let R and S be symmetric relations on a set A

Is R ⊕ S symmetric?

Back 2

Yes

Front 3

Let R and S be symmetric relations on a set A

Is R \ S symmetric?

Back 3

Yes

Front 4

Let R and S be symmetric relations on a set A

Is R ◦ S symmetric?

Back 4

No

Front 5

Let R and S be symmetric relations on a set A

Is R^(-1) symmetric?

Back 5

Yes

Front 6

Let R and S be symmetric relations on a set A

Is R^n, n ≥ 2 symmetric?

Back 6

Yes

Front 7

Let R be a transitive relation on A. Is r(R) also transitive?

Back 7

Yes

Front 8

Let R be the relation on Z defined by xRy if |x|<=y. Whats the first step to finding R-1

Back 8

|x|<=y <=> -y<= x <= y

Front 9

If R is transitive, is R^n also transitive?

Back 9

Yes

Front 10

IF F^j=R^k for some j

Back 10

Yes

Front 11

Let R be a relation on A. What is the transitive closure of R?

Back 11

R^*