Prove or disprove that DomS composed of RDomRSolutionIf R is

Prove or disprove that Dom(S composed of R)=Dom(R)

Solution

If R is a subset of Across B and S is subset of B cross C then

S0R={(a,c)belongs to A cross C; there exists b inB such that (a,b) belongs to R and( b,c) belongs to S}

For eg Let A={1,2,3}

let B={3,5,6}

let C={7,8,9}

Let R be a relation from A to Bso R is a subset of A cross B

R={ (1,3) (2,5)( (3,3)}

S be a relation from B to C so S is a subset of B cross C

S={(3,8) (3,9) (6,8)}

S composite R ={(1,8) (1,9) (3,8) (3,9)}

Domain of An ordered pair is the first number in every pair

Domain Of S composite R={1,3}

Domain Of R={1,2,3}

Hence domain of S composite R is a subset of domain R