Question

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})} 

Answer 1

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)