Translate the following propositions into English. Assume our domain, D, are the

Question

Translate the following propositions into English. Assume our domain, D, are the integers. Give your answer in the most concise and natural way you can think of. Are these statements equivalent? Why or why not? (a) ForAll v Exists w, x, y, z [(v > 0) rightarrow (v = w^2 + x^2 + y^2 + z^2)] (b) Exists w, x, y, z, ForAll v [(v > 0) rightarrow (v = w^2 + x^2 + y^2 + z^2)] Use predicates, quantifiers, and logical connectives to translate the following: A passenger on United Airlines qualifies as an elite flyer if the passenger has traveled more than 25, 000 miles in a year or takes more than 25 flights during that year. DO NOT use the numbers 25, 000 or 25 in the predicates. Assume our Domain is passengers and positive integers.

Explanation / Answer

(1)

(a) For each value of v ,there is atleast one value of w, x ,y ,z such that value of v is greater than zero implies v is equal to sum of squares of w , x ,y and z.

(b) There is atleast one value of w, x ,y ,z for each value of v such that value of v is greater than zero implies v is equal to sum of squares of w,x,y,z.

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