Question
Which conditional statement is represented by the Venn diagram below? A. If a shape has three vertices, then it is a triangle. B. If a shape is a triangle, then it does not have three vertices. C. If a shape is a triangle, then it has three vertices. D. If a shape does not have three vertices then it is a triangle.
Answer
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(257 Votes)
Joseph
Elite · Tutor for 8 years
Answer
To determine which conditional statement is represented by the Venn diagram, we need to understand the relationship between the two sets represented by the circles.Step 1: Identify the sets in the Venn diagram.- The orange circle represents the set of shapes with "Three vertices."- The blue circle represents the set of shapes that are "Triangles."Step 2: Understand the relationship between the sets.- The Venn diagram typically shows the overlap between two sets. If the blue circle (Triangles) is entirely within the orange circle (Three vertices), it means that all triangles have three vertices, but not all shapes with three vertices are necessarily triangles.Step 3: Match the relationship to the correct conditional statement.- A conditional statement has the form "If P, then Q," where P is a condition that leads to Q.Step 4: Evaluate the options.A. If a shape has three vertices, then it is a triangle.- This statement is not necessarily true because there could be shapes with three vertices that are not triangles (e.g., a shape that is not closed).B. If a shape is a triangle, then it does not have three vertices.- This statement is false because by definition, a triangle must have three vertices.C. If a shape is a triangle, then it has three vertices.- This statement is true because all triangles, by definition, have three vertices.D. If a shape does not have three vertices, then it is a triangle.- This statement is false because there are many shapes that do not have three vertices and are not triangles.Step 5: Extract the final answer.- The correct conditional statement represented by the Venn diagram is:C. If a shape is a triangle, then it has three vertices.