4. Suppose T is a set of natural numbers, and we have the following statement about T. S₁: 2 is the only prime number that divides elements of T. Which of the following statements imply S₁? Which are implied by S₁? For each case, give a brief justification. (a) S₂: T is the set of all natural numbers that satisfy the quadratic equation x² + x + 1 = 0. (b) S3: T (16,8, 528). (c) S4: All elements of T are equal to 2", where n is a natural number. (d) S5: If i, jT, and i

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