Question

If A = {2,5,6}, B = {3,5,8, 2}, C = {6,8,9), find (i) A U (BNC),
(ii) AN (BUC) (iii) A - (BUC).​

Answer 1

Given :-

$\bullet \sf \ A = \{ 2,5,6 \} \\\\\bullet \ B = \{3,5,8,2 \} \\\\\bullet \ C = \{ 6,8,9 \}$

( i )

$\longrightarrow \sf A \cup (B\cap C )\\\\\longrightarrow (A \cup B) \cap (A \cup c) \\\\\longrightarrow( \{2,5,6 \} \cup \{3,5,8,2 \} ) \cap ( \{2,5,6 \} \cup \{6,8,9 \} ) \\\\\longrightarrow \{ 2,3,5,6,8 \} \cap \{2,5,6,8,9\}\\\\\longrightarrow \bf \{2,5,6,8 \}$

( ii )

$\longrightarrow \sf A \cap ( B \cup C ) \\\\\longrightarrow (A \cap B ) \cup ( A \cap C ) \\\\\longrightarrow ( \{2,5,6 \} \cap \{3,5,8,2 \} ) \cup ( \{2,5,6 \} \cap \{6,8,9 \} )\\\\\longrightarrow \{ 2,5 \} \cup \{6 \} \\\\\longrightarrow\bf \{ 2 , 5 , 6 \}$

( iii )

$\longrightarrow \sf A-( B \cup C ) \\\\\longrightarrow (A-B) \cap ( A-C) \\\\\longrightarrow ( \{2,5,6 \} - \{3,5,8,2 \} ) \cap ( \{2,5,6 \} -\{6,8,9 \} ) \\\\\longrightarrow \{6\} \cap \{2,5 \} \\\\\longrightarrow \bf \{ \phi\}$