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Problem: Construct the disjunctive normal form of function \( f \). 1) \( f\left(x^{4}\right)=(1011010110110101) \); 2) \( f\left(x^{4}\right)=(0101111101011111) \).

6.3.14 Boolean algebra

2.03 $

Problem: Construct the conjunctive normal form of function \( f \). 1) \( f\left(x^{4}\right)=(1001011100011010) \); 2) \( f\left(x^{4}\right)=(1011000110101110) \).

6.3.15 Boolean algebra

2.03 $

Problem: Find the cardinality of the set \[ A=(L \cap S) \backslash\left(T_{0} \cap T_{1}\right), \] where \( L, S, T_{0}, T_{1} \) are Post classes.

6.3.16 Boolean algebra

3.81 $

Problem: Find the power of the set of Boolean functions of \( n \) variables \( A=\left(T_{0} \cap T_{1}\right) \cup(L \backslash S) \), where \( L, S, T_{0}, T_{1} \) are Post classes.

6.3.17 Boolean algebra

3.81 $

Problem: Find the power of the set of Boolean functions with \( n \) variables. \( A=(L \backslash S) \cup\left(T_{0} \backslash T_{1}\right) \), where \( L, S, T_{0}, T_{1} \) are Post classes.

6.3.18 Boolean algebra

3.81 $

Problem: Find three non-isomorphic spanning trees. In the case of a disconnected graph, spanning trees should be found for the larger component.

6.4.9 Graph theory

2.03 $

Problem: Find the spanning tree of the minimum weight of the graph. The weights of the edges are shown in the graph.

6.4.10 Graph theory

2.54 $

Problem: Find the main characteristics of the graph (vertex eccentricities, vertex degrees, adjacency matrix, vertex and edge connectivity numbers, radius, diameter and diametrical chain, density and looseness, chromatic number) represented by the figure. In the case of a disconnected graph, the characteristics should be found for the larger component.

6.4.11 Graph theory

3.81 $

Problem: Find three non-isomorphic spanning trees. In the case of a disconnected graph, spanning trees must be found for the larger component.

6.4.12 Graph theory

2.03 $

Problem: Find the spanning tree of the minimum weight of the graph. The weights of the edges are given in the graph.

6.4.13 Graph theory

2.54 $

Problem: Find the main characteristics of the graph (vertex eccentricities, vertex degrees, adjacency matrix, vertex and edge connectivity numbers, radius, diameter and diametrical chain, density and looseness, chromatic number) represented by the figure. In the case of a disconnected graph, the characteristics should be found for the larger component.

6.4.14 Graph theory

3.81 $

Problem: Find three non-isomorphic spanning trees of the graph. In the case of a disconnected graph, spanning trees should be found for the larger component.

6.4.15 Graph theory

2.03 $

Problem: Find the spanning tree of the minimum weight of the graph. The edge weights are shown in the graph.

6.4.16 Graph theory

2.54 $

Problem: Find the main characteristics of the graph (vertex eccentricities, vertex degrees, adjacency matrix, vertex and edge connectivity numbers, radius, diameter and diametrical chain, density and looseness, chromatic number) represented by the figure. In the case of a disconnected graph, the characteristics should be found for the larger component.

6.4.17 Graph theory

3.81 $

Problem: Find three non-isomorphic spanning trees of the graph. In the case of a disconnected graph, spanning trees must be found for the larger component.

6.4.18 Graph theory

2.03 $

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