Problem:** A mathematician models a food web with 120 organisms: 70 are herbivores, 60 are insectivores, and 25 are both. How many organisms are only herbivores (not insectivores)?

["Title: How to Calculate the Number of Organisms That Are Only Herbivores in a Food Web Model", "When modeling complex ecosystems, understanding the relationships between different organism types is essential. A recent mathematical analysis of a food web involving 120 organisms revealed a nuanced distribution among herbivores and insectivores, prompting an important question: How many organisms are exclusively herbivores (i.e., herbivores that do not eat insects)?", "### The Problem Breakdown", "In this food web model, the data is as follows:", "- Total organisms: 120\n- Herbivores (H): 70\n- Insectivores (I): 60\n- Organisms that are both herbivores and insectivores (H ∩ I): 25", "We aim to determine how many organisms belong only to the herbivore group—those who consume plants but not insects. This means we want the number of organisms in H only, or mathematically, H − (H ∩ I).", "### Step-by-Step Calculation", "1. Identify the number of organisms that are exclusively herbivores:\n [\n \ ext{Only Herbivores} = |H| - |H \cap I|\n ]\n Substituting the values:\n [\n \ ext{Only Herbivores} = 70 - 25 = 45\n ]", "2. Interpretation:\n Out of the 70 classified as herbivores, 25 overlap with insectivores—meaning 45 herbivores consume only plants and do not prey on insects.", "3. Verification:\n An additional check confirms consistency. Total herbivores includ both those only eating plants (45) and those that supplement with insects (25), summing correctly to 70. Insectivores total 60, of which 25 are shared, leaving 35 insectivores that are exclusive herbivores—however, this exceeds our original herbivore count, reinforcing our model consistency.", "### Why This Matters in Mathematical Ecology", "Modeling overlapping roles helps assess competition, energy flow, and species interactions in food webs. Knowing precise subgroup counts—such as 45 exclusive herbivores—refines predictions about ecosystem stability and resource use.", "### Summary", "In this well-structured food web model with:", "- Herbivores: 70\n- Insectivores: 60\n- Both herbivores and insectivores: 25", "The number of organisms that are only herbivores (not insectivores) is:", "45", "Using set theory fundamentals, this calculation ensures accurate representation and deeper insight into the system’s architecture.", "---", "Keywords: food web model, herbivores in ecology, insectivores vs herbivores, overlapping sets in food chains, mathematical ecology, ecosystem modeling, H ∩ I calculation, exclusive herbivores."]