Let U be a set and let P be an open statement with domain U. Let A = {x U: P(x) is true}, i.e., the truth set of P. Let a U be fixed. Are the following true or false? Explain your answers. (a) If a A, then we may deduce that P(a) is true. (b) If P(a) is true, then we may deduce that a A. (c) If ~P(a) is true, then we may deduce that a & A. (d) If a A, then we may deduce that ~P(a) is true.