1 \(\mathrm{A}-\mathrm{B}=\{1,2\}\)
2 \(\mathrm{B}-\mathrm{A}=\{5,6\}\)
3 \([(\mathrm{A}-\mathrm{B})-(\mathrm{B}-\mathrm{A})] \cap \mathrm{A}=\{1,2\}\)
4 \([(\mathrm{A}-\mathrm{B})-(\mathrm{B}-\mathrm{A})] \cup \mathrm{A}=\{3,4)\)
Explanation:
,b,c) : Given, \(\mathrm{A}=\{1,2,3,4\}\)
\(\mathrm{B}=\{3,4,5,6\}\)
Then, by options -
Options a :-
\(A-B=\{1,2,3,4\}-\{3,4,5,6\}\)
\(A-B=\{1,2\}\)
\(B-A=\{3,4,5,6\}-\{1,2,3,4\}\)
\(=\{5,6\}\)
Option b :-
\(\mathrm{B}-\mathrm{A}=\{3,4,5,6\}-\{1,2,3,4\}\)
Options c :-
\([(\mathrm{A}-\mathrm{B})-(\mathrm{B}-\mathrm{A})] \cap \mathrm{A}\)
\(=[\{1,2\}-\{5,6\}] \cap\{1,2,3,4\}\)
\(=\{1,2\} \cap\{1,2,3,4\}\)
\(=\{1,2\}\)
Option d :-
\({[(\mathrm{A}-\mathrm{B})-(\mathrm{B}-\mathrm{A})] \cup \mathrm{A}}\)
\(=[\{1,2\}-\{5,6\}] \cup\{1,2,3,4\}\)
\(=\{1,2,\} \cup\{1,2,3,4\}\)
\(=\{1,2,3,4\} .\)So, we see that option (a, b, c) are correct.