Question

if AUB=(p,q,r,s) , AUC= (q,r,s,t) A∩C=(q,s) Find A,B and C

Answer 1

A⋂C={q,s}⇒A and C both contain q and s. So A={q,s,...}, C={q,s,...}, but A and C have no other elements in common.

A⋃C={q,r,s,t}⇒either A or C, but not both, contain r and/or t.

A⋃B={p,q,r,s}⇒either A or B, but not both, contain p and/or r.

These taken together imply that r∈A, so t∈C. Also p∈B.

If C={q,s,t} and A={q,r,s}, then B={p,q,s} or {p} or {p,q} or {p,s}.

A⋃C={q,r,s,t}; A⋂C={q,s}; A⋃B={p,q,r,s}; A⋂B={q,s} or {} or {q} or {s}.