Mathematics

Problem

4. Show that the following four conditions are equivalent: (i)

\mathrm{A} \subset \mathrm{B}

(ii)

\mathrm{A}-\mathrm{B}=\phi

(iii)

\mathrm{A} \cup \mathrm{B}=\mathrm{B}

(iv)

\mathrm{A} \cap \mathrm{B}=\mathrm{A}