Question

show that (aub)-c=(a-c)u(b-c)

Answer 1

Answer:

TO PROOF:(AUB)-C=(A-C)U(B-C)

let ,A={x,y,z}

B={u,v,w,x}

C={y,v,p,q}

L.H.S=(AUB)-C

(AUB)={x,y,z}U{u,v,w,x}

={u,v,w,x,y,z}

C={y,v,p,q}

Therefore,(AUB)-C={u,v,w,x,y,z}-{y,v,p,q}

={u,w,x,z}

RHS=(A-C)U(B-C)

(A-C)={x,y,z}-{y,v,p,q}

={x,z}

(B-C)={u,v,w,x}-{y,v,p,q}

={u,w,x}

Therefore,

(A-C)U(B-C)={x,z}U{u,w,x}

={u,w,x,z}

Therefore,

LHS=RHS

HENCE SHOWED.

HOPE IT WILL HELP YOU.

IF ANYTHING IS INCORRECT THEN CORRECT ME PLZ.