For the following statement, give proofs using the indicated method. First identify your premises and conclusion....

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For the following statement, give proofs using the indicated method. First identify your premises and conclusion. Convert them into predicates or propositions. Then prove the conclusion with the premises and the rule. • Statement 1: For positive real number a, x + 1 ≥ 2. • Statement 2: For x, y Z, if both x² + y² and ry are even, then both r and y are even. • Statement 3: 2³+2r²-2-4-0 has a solution in (1,2). 1. For statement 1, prove using Direct Proofs, Contradiction and Proof by cases. For the following statement, give proofs using the indicated method. First identify your premises and conclusion. Convert them into predicates or propositions. Then prove the conclusion with the premises and the rule. • Statement 1: For positive real number a, x + 1 ≥ 2. • Statement 2: For x, y Z, if both x² + y² and ry are even, then both r and y are even. • Statement 3: 2³+2r²-2-4-0 has a solution in (1,2). 1. For statement 1, prove using Direct Proofs, Contradiction and Proof by cases.