Let P(m, n) be the statement \"m divides n\". Let the domain of m and n be the s

Question

Let P(m, n) be the statement "m divides n". Let the domain of m and n be the set of positive integers. For each of the statements below, do the following: (i) express it in terms of quantifiers and P(m, n) and (ii) determine if the statement is true or false. Note that the word "number" refers to any positive integer. a. There is a number that divides every positive integer. b. Every number cannot divide some other positive integer. c. Every number that is divisible by 9 is also divisible by 3. d. The only number that is divisible by 5 and 7 is 35.

Explanation / Answer

m divides n
a.there is a number that divides every positive number
n m P(m, n)-True,True as we can always choose m = 1
b.every number cannot divide some other positive number
True.Ex:P(4,5)
c.Every num divisible by 9 is also divisible by 3
(x n)(m )P(m, n) where n={multiples of 9}-True
d.The only number that is divisible by 7 and 5 is 35
True.

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