Math Problems and solutions
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6.2.16 Binary relations
3.82 $
6.2.17 Binary relations
1.78 $
6.2.18 Binary relations
6.2.19 Binary relations
1.27 $
![Problem: Two finite sets are given: \( A=\{a, b, c\}, B=\{1,2,3,4\} \); binary relations are \( P_{1} \subseteq A \times B ; P_{2} \subseteq B^{2} \). Represent \( P_{1}, P_{2} \) graphically. Find \( P=\left(P_{2} \circ P_{1}\right)^{-1} \). Write the domains of definition and ranges of all three relations: \( P_{1}, P_{2}, P \). Construct the matrix \( \left[P_{2}\right] \), use it to check if the relation \( P_{2} \) is reflexive, symmetric, antisymmetric, transitive. \[ \begin{array}{l} P_{1}=\{(a, 1),(b, 3),(c, 1),(c, 4),(c, 3),(c, 2)\} ; \\ P_{2}=\{(1,1),(1,2),(1,4),(2,1),(2,2),(2,3),(3,3), \\ (3,2),(3,4),(4,3),(4,4),(4,1)\} . \end{array} \]](/storage/uploads/task_mls/1594/en/6.2.16.png){kind=link}
![Problem: Two finite sets are given: \( A=\{a, b, c\}, B=\{1,2,3,4\} \); binary relations are \( P_{1} \subseteq A \times B ; P_{2} \subseteq B^{2} \). Represent \( P_{1}, P_{2} \) graphically. Find \( P=\left(P_{2} \circ P_{1}\right)^{-1} \). Write the domains and ranges of all three relations: \( P_{1}, P_{2}, P \). Construct the matrix \( \left[P_{2}\right] \), use it to find out if the relation \( P_{2} \) is reflexive, symmetric, antisymmetric, transitive. \[ \begin{array}{l} P_{1}=\{(a, 3),(a, 2),(a, 4),(b, 1),(c, 4),(c, 3),(c, 2)\} \\ P_{2}=\{(1,1),(1,4),(2,1),(2,2),(2,4),(3,3),(4,4), \\ (4,3),(3,2),(3,4)\} \end{array} \]](/storage/uploads/task_mls/1596/en/6.2.18.png){kind=link}
