Question

1. Write down the following sentences in predicate logic.

a) Every positive real number has a unique positive real square root.

b) The equation x² + 2x + 1 = 0 has no solutions over the natural numbers.

For a, I was also wondering because it mentions "unique" if that would change the answer (i.e. use the ∃! symbol that was mentioned in my lecture).

2. "Every real number is non-negative unless it is less than 1.”

Translate this sentence into symbols (such as ?, ?, ∃, ∀, <, ≤, →,⋀ ,???.)

I'm kind of confuse on how to approach this question and how to convert it into symbols.

Answer 1

Solution

1

a)

we can write this answer many different ways

one of the way is

consider the domain is the set of positive real numbers

Predicate Sq(x,y) will be true if x=y² otherwise it will be false

b)

--

answered first part, really sorry for that

please post remaining question separately, love to answer

all the best