Determine the truth values of the following symbolized statements. Let A, B, and C betrue and X,Y, and Z be false1. (A • Y) v (~Z • C)2. ~(X v ~B) • (~Y v A)

Sure, I can help you determine the truth values of the symbolized statements.

1. (A • Y) v (~Z • C):

   • Given that A is true and Y is false, we can substitute these values into the statement: (true • false) v (~Z • C).
   • Since the conjunction (•) requires both statements to be true in order for the whole statement to be true, the first part (A • Y) is false.
   • Now, we can substitute the values into the second part: (~Z • C).
   • Given that Z is false and C is true, we have: (~false • true).
   • The negation (~) of false is true, so we have: (true • true).
   • Since the conjunction (•) requires both statements to be true in order for the whole statement to be true, the second part (~Z • C) is true.
   • Finally, we have: false v true.
   • The disjunction (v) requires at least one statement to be true in order for the whole statement to be true, so the final truth value is true.

2. ~(X v ~B) • (~Y v A):

   • Given that X is false and B is true, we can substitute these values into the statement: ~(false v ~true) • (~Y v A).
   • The negation (~) of false is true, and the negation (~) of true is false, so we have: ~(false v false) • (~Y v A).
   • The disjunction (v) requires at least one statement to be true in order for the whole statement to be true, so we have: ~(false) • (~Y v A).
   • The negation (~) of false is true, so we have: true • (~Y v A).
   • Given that Y is false and A is true, we can substitute these values into the second part: true • (~false v true).
   • The negation (~) of false is true, so we have: true • (true v true).
   • The disjunction (v) requires at least one statement to be true in order for the whole statement to be true, so we have: true • true.
   • The conjunction (•) requires both statements to be true in order for the whole statement to be true, so the final truth value is true.