The negation of a statement is the opposite of that statement. In this case, the opposite of "All dogs are mammals" is "No dogs are mammals".

The conjunction of two statements is a new statement that is true if and only if both of the original statements are true. In this case, both "The sky is blue" and "The grass is green" are true, so their conjunction is also true.

The disjunction of two statements is a new statement that is true if either of the original statements is true. In this case, either "I am happy" or "I am sad" is true, so their disjunction is also true.

Using truth tables, we can determine that the statement "(¬P ∨ Q) → (P ∧ Q)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P → Q) ∧ (Q → R)" is true in all cases except when P is true and Q is false. Therefore, the statement is true.

Using truth tables, we can determine that the statement "¬(P ∧ Q) → (¬P ∨ ¬Q)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P ∨ Q) → (¬P → Q)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P → Q) ∨ (¬Q → P)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P ∧ Q) → (P ∨ Q)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P ∨ Q) → (P ∧ Q)" is false when P is true and Q is false.

Using truth tables, we can determine that the statement "¬(P → Q) → (P ∧ ¬Q)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P ∧ Q) ∨ (¬P ∧ ¬Q)" is always true, regardless of the truth values of P and Q.

Using truth tables, we can determine that the statement "(P → Q) → ((¬P ∨ R) → Q)" is always true, regardless of the truth values of P, Q, and R.

Using truth tables, we can determine that the statement "(P ∨ Q) → ((P → R) ∧ (Q → R))" is always true, regardless of the truth values of P, Q, and R.

Using truth tables, we can determine that the statement "(P → Q) → ((¬Q → ¬P) ∧ (¬P → ¬Q))" is always true, regardless of the truth values of P and Q.