Question: Consider binary relationsR, S, T. Prove the following: (a)(RS) 1 =R 1 S 1 . (b)(RS) 1 =R 1 S 1 . (c)T(RS)=(TR)(TS). (d)T(RS)(TR)(TS). Consider

Consider binary relationsR, S, T. Prove the following:

(a)(RS)1=R1S1.

(b)(RS)1=R1S1.

(c)T(RS)=(TR)(TS).

(d)T(RS)(TR)(TS).

Consider binary relationsR, S, Tand setsX, Y. Prove the following:

(a)(SR)[X] =S[R[X]].

(b)R[XY]=R[X]R[Y].

(c)XR1[R[X]].

(d)AssumeRis a function. Prove thatR1[XY] =R1[X]R1[Y].

(e)Consider a setAand the binary relationRAP(A) defined by

x,XRxX

GivenX,YP(A), calculateR1[{X}] andR1[{X, Y}].

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