Which one of the following relations represents the composition relation P ○ P (ie P; P)? 1. {(a, {a, b}), (b, a), ({a, b}, a), ({b}, {a}), (a, {a})} 2. {(a, {a, b}), (b, a), ({a, b}, a), ({b}, {a})} 3. {(a, {a, b}), (b, a), ({a, b}, {a}), ({a, b}, b), ({b}, b), ({b}, {a})} 4. {(a, {a, b}), (b, a), ({a, b}, {a}), ({a, b}, b), ({b}, {a})}
Given that,
The set B is:
"B=\\{a,b,\\{a\\},\\{b\\},\\{a,b\\}\\}"
and , the set P is:
"P= \\{(a,b),(b,\\{a,b\\}),(\\{a,b\\},a),(\\{b\\},a),(a,\\{a\\})\\}"
The composition relation "Po P" is given as :
"\\{(a,\\{a,b\\}),(b,a),(\\{a,b\\},\\{a\\}),(\\{a,b\\},b),(\\{b\\},b),(\\{b\\},\\{a\\})\\}"
Thus, the correct option is (3)
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