Discrete math 5 R and S are relations on set A11234 defined

Discrete math

5) R and S are relations on set A-11,2,3,4), defined as R (1,2,(1,3), (2,3), (2,4), (3,1), S F (2,1, (3,1), (3,2), (4,2). Find S o R, R o S, R-1, S-1,where o means composition

Solution

SoR = {(1,1),(1,1),(1,2),(2,1),(2,2),(2,2)}

therefore SoR={(1,1),(1,2),(2,1),(2,2)}

RoS={(2,2),(2,3),(3,2),(3,3),(3,3),(3,4)}

therefore RoS={(2,2),(2,3),(3,2),(3,3),(3,4)}

R^-1={(2,1),(3,1),(3,2),(4,2),(1,3)}

S^-1={(1,2),(1,3),(2,3),(2,4)}