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Question: math 430 hw due 123 1 for each of the...

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MATH 430- HW Due 1-23 1. For each of the following statements, complete the following a. Determine whether the statement is true or false (we call this the truth value of the statement b. For true statements, determine how many numbers satisfy the described condition for the number a (e.g.- one a for all x, one a for each x, many a for each х). Does the value of a “depend upon the value of x? For false statements, write out what it means for the statement to be false (the negation of the statement) and explain why this negation is c. true i. ii. iii. iv. V. vi. VxER,3 a E R such that x + a 0 ヨa E R, such that V x E R, x + a = 0 VxER,3a E R such that xa 0 a E R, such that V x E R, x * a-0 VxER,3aERsuch that x *a=1 ヨa E R, such that Vx E R, x * a = 1 2. Imagine two MATH 430 students were discussing their answers to problems li and lii. Cyan said that he can show that statement li is true by letting a--х. Ronso responded that he thought statement li must be true by the same reasoning. Which of these students answers is mathematically appropriate and why? (Hint: one is appropriate and one is not) Try to be as clear and precise as you can in your explanation. Clearly this value of a makes the equation in both statements true, so try to explain how the quantifiers influence the way we think about the numbers x, a, and - x

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