Find n(A ext ext extbar } B), n(B ext ext extbar } A), n(A ext ext extbar } B^c) and n(A^c ext ext extbar } B) given n(A)=10, n(B)=7, n(A ext ext extbar } B)=8 and n(U)=15.

Here are the solutions to the problems: 1. Find n(A B) if sets A and B have n(A) = 10, n(B) = 7 and n(A B) = 9. Step 1: Use the formula for the number of elements in the union of two sets. n(A B) = n(A) + n(B) - n(A B) Step 2: Substitute the given values into the formula. 9 = 10 + 7 - n(A B) Step 3: Simplify the equation. 9 = 17 - n(A B) Step 4: Solve for n(A B). n(A B) = 17 - 9 n(A B) = 8 The number of elements in the intersection of A and B is 8. 2. Find the value of x if _x 4 = 2. Step 1: Convert the logarithmic equation to an exponential equation. The definition of a logarithm states that _b a = c is equivalent to b^c = a. x^2 = 4 Step 2: Solve for x. Take the square root of both sides. x = ±sqrt(4) x = ± 2 Step 3: Consider the domain of the logarithm. The base of a logarithm must be positive and not equal to 1. Therefore, x > 0 and x 1. x = 2 The value of x is 2. 3. Simplify [4]x^9 y^7[4]xy^-5. Step 1: Combine the terms under a single fourth root, using the property n]a[n]b = [n/(b). 4]x^9 y^7[4]xy^-5 = [4/(xy^-5) Step 2: Simplify the expression inside the root using exponent rules (a^m)/(a^n) = a^m-n. [4]x^9-1 y^7-(-5) [4]x^8 y^7+5 [4]x^8 y^12 Step 3: Rewrite the radical expression using fractional exponents, [n]a^m = a^m/n. (x^8 y^12)^1/4 Step 4: Apply the exponent to each term inside the parentheses, using (ab)^n = a^n b^n and (a^m)^n = a^mn. x^8 · (1)/(4) y^12 · (1)/(4) x^2 y^3 The simplified expression is x^2 y^3.