Chapter 6 - Set Theory - Exercise Set 6.3 - Page 373: 46

$a-\,\,\\ A\bigtriangleup B=\left \{ 1,2,5,6 \right \}\\$ $b-\,\,\\ B\bigtriangleup C= \left \{ 3,4,7,8 \right \}\\$ $c-\,\,\\ A\bigtriangleup C=\left \{ 1,2,3,4,5,6,7,8 \right \}\\$ $d-\,\,\\ (A\bigtriangleup B)\bigtriangleup C= \left \{ 1,2,7,8 \right \}$

$A=\left \{ 1,2,3,4 \right \},B=\left \{ 3,4,5,6 \right \},C=\left \{ 5,6,7,8 \right \}\\ A-B=\left \{ 1,2 \right \},B-A=\left \{ 5,6 \right \}\\ A\bigtriangleup B= (A - B) \cup (B - A) \\ A\bigtriangleup B=\left \{ 1,2 \right \}\cup \left \{ 5,6 \right \}=\left \{ 1,2,5,6 \right \}\\ B-C=\left \{3,4 \right \},C-B=\left \{ 7,8 \right \}\\ B\bigtriangleup C= (B - C) \cup (C - B) \\ B\bigtriangleup C= \left \{ 3,4 \right \}\cup \left \{ 7,8 \right \}=\left \{ 3,4,7,8 \right \}\\ A-C=\left \{1,2,3,4 \right \},C-A=\left \{ 5,6,7,8 \right \}\\ A\bigtriangleup C= (A - C) \cup (C - A) \\ A\bigtriangleup C= \left \{ 1,2,3,4 \right \}\cup \left \{ 5,6,7,8 \right \}\\ A\bigtriangleup C=\left \{ 1,2,3,4,5,6,7,8 \right \}\\ $ $(A\bigtriangleup B)\bigtriangleup C=((A\bigtriangleup B)- C)\cup (C-(A\bigtriangleup B))\\ A\bigtriangleup B=\left \{ 1,2,5,6 \right \},C=\left \{ 5,6,7,8 \right \}\\ (A\bigtriangleup B)- C =\left \{ 1,2 \right \}\\ C-(A\bigtriangleup B)=\left \{ 7,8 \right \}\\ (A\bigtriangleup B)\bigtriangleup C=((A\bigtriangleup B)- C)\cup (C-(A\bigtriangleup B))\\ (A\bigtriangleup B)\bigtriangleup C=\left \{ 1,2 \right \}\cup \left \{ 7,8 \right \}= \left \{ 1,2,7,8 \right \}$