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7. (a) -(A= B) is logically equivalent to (-A) = (-B). (b) -( V ES, P(x)) is logically equivalent to Va e S.-P()). (c) If a, b, c, d e Z, ab, bc, and cd, then ad. (d) If a, b, c e Z, and a be, then a b or a c. ( 1 cos 1 + i sin ) 1- į 2 +2 (f) A polar form of the complex number z = -18i is 18(cos( + isin ). (g) god (29931005101 29831005102) = 29831005101
8. Let P and Q be two mathematical statements. The statement -(PA(Q)) is equivalent to ... • (-P)^(-Q) • (-P) V(-Q) • (-P) VQ . P^(-Q)
5. (a) The negation of A B is AV-B). (b) The polynomial r3 - 3x² + x + 2 has a rational root. (c) 75 is a valid n in the RSA encryption scheme. (d) If f(z) is a polynomial with complex coefficients and z = i is a root of f(z), then z =-i must also be a root of f(z). (e) A B is logically equivalent to (-B) = (-A). (f) 1 + i is an eighth root of unity.
