1. "Every simple graph with 5 vertices and 4 edges is a tree." - This statement is true. A simple graph with n vertices and n-1 edges without any cycles is a tree.

2. "Every connected graph with 8 vertices and 9 edges is a tree." - This statement is false. A tree is a connected graph with no cycles. If a graph has n vertices and n-1 edges, it is a tree. Here, the graph has 8 vertices and 9 edges, which means it has one cycle and hence, it is not a tree.

3. "Every simple connected graph with 6 vertices and 7 edges is a tree." - This statement is false. A tree is a connected graph with no cycles. If a graph has n vertices and n-1 edges, it is a tree. Here, the graph has 6 vertices and 7 edges, which means it has one cycle and hence, it is not a tree.

4. "Every tree with 11 vertices is simple, connected and has 10 edges." - This statement is true. A tree is a simple, connected graph with no cycles. If a graph has n vertices, it will have n-1 edges. Hence, a tree with 11 vertices will have 10 edges.

Question

1. "Every simple graph with 5 vertices and 4 edges is a tree." - This statement is true. A simple graph with n vertices and n-1 edges without any cycles is a tree.

2. "Every connected graph with 8 vertices and 9 edges is a tree." - This statement is false. A tree is a connected graph with no cycles. If a graph has n vertices and n-1 edges, it is a tree. Here, the graph has 8 vertices and 9 edges, which means it has one cycle and hence, it is not a tree.

3. "Every simple connected graph with 6 vertices and 7 edges is a tree." - This statement is false. A tree is a connected graph with no cycles. If a graph has n vertices and n-1 edges, it is a tree. Here, the graph has 6 vertices and 7 edges, which means it has one cycle and hence, it is not a tree.

4. "Every tree with 11 vertices is simple, connected and has 10 edges." - This statement is true. A tree is a simple, connected graph with no cycles. If a graph has n vertices, it will have n-1 edges. Hence, a tree with 11 vertices will have 10 edges.

Knowee AI · Accepted Answer

1. "Every simple graph with 5 vertices and 4 edges is a tree." - This statement is true. A simple graph with n vertices and n-1 edges without any cycles is a tree.

2. "Every connected graph with 8 vertices and 9 edges is a tree." - This statement is false. A tree is a connected graph with no cycles. If a graph has n vertices and n-1 edges, it is a tree. Here, the graph has 8 vertices and 9 edges, which means it has one cycle and hence, it is not a tree.

3. "Every simple connected graph with 6 vertices and 7 edges is a tree." - This statement is false. A tree is a connected graph with no cycles. If a graph has n vertices and n-1 edges, it is a tree. Here, the graph has 6 vertices and 7 edges, which means it has one cycle and hence, it is not a tree.

4. "Every tree with 11 vertices is simple, connected and has 10 edges." - This statement is true. A tree is a simple, connected graph with no cycles. If a graph has n vertices, it will have n-1 edges. Hence, a tree with 11 vertices will have 10 edges.

Which of the following is true?Every simple graph with 5 vertices and 4 edges is a tree.Every connected graph with 8 vertices and 9 edges is a tree.Every simple connected graph with 6 vertices and 7 edges is a tree.Every tree with 11 vertices is simple, connected and has 10 edges.unanswered

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