please answer 7ab and 8ab and I will rate. Write each of the following formal st
ID: 3111814 • Letter: P
Question
please answer 7ab and 8ab and I will rate.
Write each of the following formal statements informally (without quantifiers and without variables). For each, provide two non-identical, yet equivalent, responses. (a) ForAll x elementof Z, x^2 elementof Z. (b) exist a Texan x such that x works for NASA. Write each of the following informal statements formally (with quantifiers and variables) and write the negation of each, first formally, then informally. If an integer is even, then that integer is positive. Some customer ate all of the pies in the display case.Explanation / Answer
7)
a) Informal statement: The square of every integer is also an integer.
Equivalent statement 1: The square of a number is an integer, if and only if the number is an integer itself.
Equivalent statement 2: There is no integer whose square is not an integer.
b)In formal statement : There are some Texans who work for NASA.
Equivalent Statement 1: There is at least one Texan who works for NASA
Equivalent Statement 2: Not every Texan works for NASA.
8)
a) Formal statement: xZ, 2x>0
Formal negation: xZ, (2x)<0
Informal Negation: There exists atleast one integer, such that if it is even, it is not positive.
b)
Formal statement: Customer is x, such that x ate all the pies.
Formal negation: Customer is x, such that x did not eat all the pie.
Informal Negation: All the customers did not eat all the pies
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