It appears that you have provided various logical expressions in different formats. To simplify these expressions and determine the truth values of F in each case, we need to break them down and evaluate them step by step.

a) F = ¬(A ∨ ¬B) → C

First, find the truth value of A ∨ ¬B.Then, find the truth value of ¬(A ∨ ¬B).Finally, determine the truth value of ¬(A ∨ ¬B) → C.

b) F = ¬(A ∧ ¬B ∧ ¬C)

First, find the truth value of A ∧ ¬B ∧ ¬C.Then, find the truth value of ¬(A ∧ ¬B ∧ ¬C).

c) F = X ∨ ¬(Y ∨ ¬(X & Y))

Break down the expression by evaluating X & Y and ¬(X & Y) separately.Find the truth values of Y ∨ ¬(X & Y).Finally, determine the truth value of X ∨ ¬(Y ∨ ¬(X & Y)).

d) F = (X ∨ Z) & (X ∨ ¬Z) & ¬X

Find the truth value of X ∨ Z.Find the truth value of X ∨ ¬Z.Find the truth value of (X ∨ Z) & (X ∨ ¬Z).Finally, determine the truth value of (X ∨ Z) & (X ∨ ¬Z) & ¬X.

e) F = (¬B → ¬A) & ¬(A ∨ B) & (A → C)

Evaluate the truth value of ¬B → ¬A.Evaluate the truth value of A ∨ B.Evaluate the truth value of (¬B → ¬A) & ¬(A ∨ B).Finally, determine the truth value of (¬B → ¬A) & ¬(A ∨ B) & (A → C).

f) F = (A & B & C) ∨ (¬A & B & C)

Find the truth values of A & B & C and ¬A & B & C.Finally, determine the truth value of (A & B & C) ∨ (¬A & B & C).

g) F = (A ∨ ¬B ∨ C) & ¬(A ∨ B ∨ C)

Find the truth value of A ∨ ¬B ∨ C.Find the truth value of A ∨ B ∨ C.Determine the truth value of (A ∨ ¬B ∨ C) & ¬(A ∨ B ∨ C).

By following these steps, you can simplify each expression and find the truth values of F in each case.