This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Recall the Principle of Inclusion-Exclusion for three sets. The formula for the number of elements in the union of three sets A, B, and C is: n(A B C) = n(A) + n(B) + n(C) - n(A B) - n(A C) - n(B C) + n(A B C) Step 2: Substitute the given values into the formula. We are given: n(A B C) = 339 n(A) = 189 n(B) = 129 n(C) = 116 n(A B) = 70 n(A C) = 58 n(B C) = 51 n(A B C) = x Substitute these values into the formula: 339 = 189 + 129 + 116 - 70 - 58 - 51 + x Step 3: Simplify the equation. First, sum the individual set sizes: 189 + 129 + 116 = 434 Next, sum the sizes of the pairwise intersections: 70 + 58 + 51 = 179 Now, substitute these sums back into the equation: 339 = 434 - 179 + x Step 4: Solve for x. 339 = 255 + x Subtract 255 from both sides: x = 339 - 255 x = 84 The value of x is 84. x = 84 Send me the next one 📸