Let U be a set and let P be an open statement with domain U. Let...

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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. 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.