I need someone to help to solve the 4 assignment below, thank you 1. Express the
ID: 3111551 • Letter: I
Question
I need someone to help to solve the 4 assignment below, thank you
1. Express the following as existence assertions:
(a) The equation x3 = 27 has a natural number solution.
(b) 1,000,000 is not the largest natural number.
(c) The natural number n is not a prime.
2. Express the following as “for all” assertions:
(a) The equation x3 = 28 does not have a natural number solution.
(b) 0 is less than every natural number.
(c) The natural number n is a prime.
3. Express the following using quantifiers. (In each case your quantifiers may
refer only to the sets R and N.)
(a) The equation x2 + a = 0 has a real root for any real number a.
(b) The equation x2 + a = 0 has a real root for any negative real number
a.
(c) Every real number is rational.
(d) There is an irrational number.
(e) There is no largest irrational number. (This one looks quite complex
4.Let C be the set of all cars, let D(x) mean that x is domestic, and let M(x)
mean that x is badly made. Express the following in symbolic form using these
symbols:
(a) All domestic cars are badly made.
(b) All foreign cars are badly made.
(c) All badly made cars are domestic.
(d) There is a domestic car that is not badly made.
(e) There is a foreign car that is badly made.
Explanation / Answer
1-
(a) x[((x)=(x^3=27)) (x)]
(b) x[(x) (x>1,000,000)]
(c) n[¬P(n)]
NOTE:- as per Chegg norms I can answer one question ( including all its subparts ) That'swhy I answered the 1st question completely.