Question

First Order Logic

Translate into First Order Logic (FOL) the following statements. Then write the negations of the FOL propositions found.
1. All tigers are fast. Domain: animals.
2. Some tigers are fierce and dangerous. Domain: animals.
3. Every prime number is odd. Domain: positive integers.
4. All prime numbers except two are odd. Domain: positive integers.
5. All fruits are either yellow or red. Domain: produce.
6. For every integer number, there exist a bigger integer. Domain: integers.

Answer 1

Answer:

1) ∀x [ Tiger(x) → Fast(x) ]

2) эx [ Tiger (x) ∧ Fierce (x) ∧ Dangerous(x) ]

3) ∀x [ Prime(x) → Odd(x) ]

4) ∀x [ prime (x) ∧ ~Two(x) → Odd (x) ]

5) ∀x [ Fruits(x) → ( yellow(x) ∨ Red(x) ]

6) ∀xэy [ I(x) → greater (y, x) ]

Step-by-step explanation:

Translating the statements into first Order Logic and their negations

1) All tigers are fast. Domain: animals.

∀x [ Tiger(x) → Fast(x) ]

2) Some tigers are fierce and dangerous. Domain: animals

эx [ Tiger (x) ∧ Fierce (x) ∧ Dangerous(x) ]

3) Every prime number is odd. Domain: positive integers

∀x [ Prime(x) → Odd(x) ]

4) All prime numbers except two are odd. Domain: positive integers

∀x [ prime (x) ∧ ~Two(x) → Odd (x) ]

5) All fruits are either yellow or red. Domain: produce.

∀x [ Fruits(x) → ( yellow(x) ∨ Red(x) ]

6) For every integer number, there exist a bigger integer. Domain: integers.

∀xэy [ I(x) → greater (y, x) ]

Step-by-step explanation:

Answer 2

1) ∀x [ Tiger(x) → Fast(x) ]

2) эx [ Tiger (x) ∧ Fierce (x) ∧ Dangerous(x) ]

3) ∀x [ Prime(x) → Odd(x) ]

4) ∀x [ prime (x) ∧ ~Two(x) → Odd (x) ]

5) ∀x [ Fruits(x) → ( yellow(x) ∨ Red(x) ]

6) ∀xэy [ I(x) → greater (y, x) ]

Step-by-step explanation:

Translating the statements into first Order Logic and their negations

1) All tigers are fast. Domain: animals.

∀x [ Tiger(x) → Fast(x) ]

2) Some tigers are fierce and dangerous. Domain: animals

эx [ Tiger (x) ∧ Fierce (x) ∧ Dangerous(x) ]

3) Every prime number is odd. Domain: positive integers

∀x [ Prime(x) → Odd(x) ]

4) All prime numbers except two are odd. Domain: positive integers

∀x [ prime (x) ∧ ~Two(x) → Odd (x) ]

5) All fruits are either yellow or red. Domain: produce.

∀x [ Fruits(x) → ( yellow(x) ∨ Red(x) ]

6) For every integer number, there exist a bigger integer. Domain: integers.

∀xэy [ I(x) → greater (y, x) ]