### Problem Statement:(c) Consider the set {0, 1, 2}.- **Task:** Verify the following statements: 1. **Original statement:** Every element in the set {0, 1, 2} is greater than or equal to half of its square. 2. **Negation:** Formulate the negation of the original statement. 3. **Assessment:** Determine which of the statements is true and provide justification.#### Instructions:1. **Original Statement:** - Analyze each element in the set {0, 1, 2} to verify if it is greater than or equal to half of its square.2. **Negation:** - Construct the negation of the original statement, which means finding an element in the set that is not greater than or equal to half of its square.3. **Evaluation:** - Assess the truth value of the original statement by checking each element in the set. - Compare this with the negation to conclude which one is true, providing mathematical reasoning for your answer.**Hint:** Use the mathematical expression \( x \geq \frac{x^2}{2} \) to test each element in the set {0, 1, 2}.

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Answered: (c) Every element in the set {0, 1, 2}…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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(c) Every element in the set {0, 1, 2} is greater than or equal to half of its square. i. Original statement: ii. Negation: iii. Which is true and why?