Using equivalence rules and methods for arguments, prove this argument is valid: (A->B)-> (AA B' -> 0)

9-x- 19-x 9-X 19-X1 tu! | 9←x cua!] X puy

For each one, state whether the statement is TRUE, FALSE. Then, state the negation:1.∃a(ais a prime number)2.∀a(ais a power of 2)3.∃a∃b(a+b <0)

Please provide a proof for the following statements(a) With domain of discourse as the real numbers, prove that the following statementis true:∀x((x > 1) → (x^2 + 4 > x + 4)) (b) With domain of discourse as the real numbers, determine if the following statement is true or false and justify your answer:∀x(x > 0 ∧ −x^2 < 0)(c) With domain of discourse as the real numbers, prove that the following statementis false:∀x∃y(y^2 < x^2 − 2)(d) State whether or not P ≡ Q, when P is the proposition (p → q) → (q ∧ r) and Qis the proposition p ∨ r. Prove the result.