Venn diagram (problem solution)

Venn diagrams, originally conceived by John Venn in the 19th century, have become a widely used tool in various fields, including biology. Their significance in biology can be attributed to several key aspects: 1. Illustrating Relationships Among Sets: Comparing Species: Biologists often use Venn diagrams to compare and contrast different species or groups of organisms. For example, they can illustrate shared and unique traits among species, facilitating studies in evolutionary biology and ecology. Gene Expression: In genomics, Venn diagrams help visualize the overlap or uniqueness in gene expression under different conditions or in different tissues. 2. Clarifying Complex Interactions: Ecological Interactions: They can represent interactions within ecosystems, such as predator-prey relationships, symbiotic relationships, or competition. Metabolic Pathways: In biochemistry, Venn diagrams can help simplify the understanding of complex metabolic pathways by showing shared or distinct metabolic processes among organisms. 3. Enhancing Data Interpretation: Statistical Analysis: In experimental biology, Venn diagrams assist in the visualization of statistical data, making it easier to interpret the results of experiments involving multiple variables or groups. Pattern Recognition: They aid in recognizing patterns in large data sets, which is essential in fields like genomics and proteomics. 4. Educational Tool: Teaching Aid: Venn diagrams are an excellent tool for teaching biological concepts, making it easier for students to grasp relationships and differences among biological groups or concepts. 5. Facilitating Research and Collaboration: Interdisciplinary Research: They enable the integration of information from different biological sub-disciplines, fostering interdisciplinary research. Communication: Venn diagrams provide a clear and concise way to communicate complex biological information, useful in research publications and presentations. 6. Identifying Evolutionary Relationships: Phylogenetics: They can be used to illustrate shared evolutionary traits among different species, aiding in the construction of phylogenetic trees and understanding evolutionary histories. 7. Bioinformatics and Systems Biology: Analyzing Big Data: In the era of big data, Venn diagrams help in the quick visualization of overlaps and differences in large data sets, such as those generated by high-throughput sequencing technologies. The significance of Venn diagrams in biology lies in their simplicity and effectiveness in visualizing complex relationships, facilitating understanding, and communication in various aspects of biological research and education. They serve as a bridge between conceptual understanding and empirical data, enhancing both the discovery process in research and the learning process in education. Problem: ξ={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} A={even numbers} B={multiples of 3} By completing the following Venn diagram, find P(A∪B′). A) 3/50 B) 3/10 C) 32/50 D) 27/50