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: Determine the expression for n(P Q) from the Venn diagram. The number of elements in P Q is the sum of elements in P only, Q only, and P Q. n(P Q) = (x - 16) + 4 + (x - 11) n(P Q) = x - 16 + 4 + x - 11 n(P Q) = 2x - 23 Step 2: Use the given condition n(P Q) = n(P Q)' to find x. From the Venn diagram, n(P Q)' = x. Substitute the expressions into the given condition: 2x - 23 = x Step 3: Solve the equation for x. Subtract x from both sides: 2x - x - 23 = 0 x - 23 = 0 Add 23 to both sides: x = 23 So, the value of x is 23. Step 4: Find n(E). The total number of elements in the universal set, n(E), is the sum of elements in P Q and elements outside P Q. n(E) = n(P Q) + n(P Q)' Since we found n(P Q) = 2x - 23 and n(P Q)' = x, and we know x=23: n(P Q) = 2(23) - 23 = 46 - 23 = 23. n(P Q)' = 23. Therefore, n(E) = 23 + 23 n(E) = 46 The value of n(E) is 46. Drop the next question 📸