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
Here's how to solve the problem: Step 1: Set up the equation for n(P Q). The total number of elements in P Q is the sum of the elements in all three regions of the Venn diagram: the elements only in P, the elements in the intersection of P and Q, and the elements only in Q. n(P Q) = (38+2x) + x + (13+x) We are given that n(P Q) = 95. 95 = 38+2x+x+13+x Step 2: Solve for x. Combine the constant terms and the terms with x: 95 = (38+13) + (2x+x+x) 95 = 51 + 4x Subtract 51 from both sides: 95 - 51 = 4x 44 = 4x Divide by 4: x = (44)/(4) x = 11 The value of x is 11. Step 3: Calculate n(P Q)'. n(P Q)' represents the number of elements that are not in the intersection of P and Q. In the context of this problem, where n(P Q) is given as the total, this means the elements within P Q but outside P Q. This is the sum of elements only in P and elements only in Q. n(P Q)' = n(P only) + n(Q only) n(P Q)' = (38+2x) + (13+x) Substitute the value of x=11: n(P Q)' = (38+2(11)) + (13+11) n(P Q)' = (38+22) + (24) n(P Q)' = 60 + 24 n(P Q)' = 84 Alternatively, n(P Q)' = n(P Q) - n(P Q). Since n(P Q) = x = 11: n(P Q)' = 95 - 11 n(P Q)' = 84 The value of n(P Q)' is 84. Send me the next one 📸