Question

Fill in the blanks to make each of the following a true statement:
(i) $A\cup A^{\prime }=...$ (ii) ${\varphi }^{\prime }\cap A=...$ (iii) $A\cap A^{\prime }=...$ (iv) $U^{\prime }\cap A=...$

Answer 1

(i) It can be clearly seen from the Venn diagram that
$A\cup A^{\prime }=U$
(ii) ${\varphi }^{\prime }\cap A=U\cap A=A$
$\therefore {\varphi }^{\prime }\cap A=A$
(iii) It can be clearly seen from the Venn diagram , there is no common portion between A and A' .
Hence, $A\cap A^{\prime }=\varphi$
(iv) $U^{\prime }\cap A=\varphi \cap A=\varphi$
$\therefore U^{\prime }\cap A=\varphi$