Answer the attached document on symbolic logic completely and correctly

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016 Do NOT put your name on the exam!

C#:

Section 1 (50 pts): Singular sentences, propositional functions and sentences with quantifiers.

• Write an appropriate symbolization for each of the following sentences (7 pts. each)

• Indicate whether they are singular sentences, propositional functions or quantified sentences (3 pts. each)

* Some things are worth waiting for.

* x is worth waiting for.

* Gottlob Frege is the father of modern predicate logic.

* Bertrand Russell is a cat.

* Everything is going to be fine.

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016 Section 2 (50 pts): Categorical sentences.

Symbolize the following categorical sentences (10 pts each):

* No human being is perfect.

* Only those who learn from their mistakes will become wise.

* Some battles are not worth fighting.

* Some moments are worth forgetting.

* Every day is a holiday.

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016

Section 3 (50 pts): Sentences with complex subjects and predicates.

List all the propositional functions in the following sentences (5 pts. each), and then symbolize the sentences (5 pts. each).

* Not all things that shine are gold, but everything that is gold shines.

Propositional functions: Symbolization:

* There are great painters that are not appreciated if they are not famous.

Propositional functions: Symbolization:

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016

* No well-paid vegetarian professional eats at McDonald’s or Burger King.

Propositional functions: Symbolization:

* Any millionaire politician who has paid taxes, hasn’t broken the law and isn’t sued will be reelected.

Propositional functions: Symbolization:

* Either John did not make a good prediction, or everyone who comes to the party and does not have an umbrella is going to be soaking wet.

Propositional functions: Symbolization:

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016 Section 4 (50 pts): Proofs in predicate logic.

Symbolize the following valid argument (25 pts), and construct a proof to show its validity (25 pts).

Be sure to justify every step in the proof!

Good mathematicians are creative and perseverant. Some mathematicians are not perseverant and not creative. Therefore, some mathematicians are not good.

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016 EXTRA CREDIT

Section 5 (20 pts): Quantifier Negation Equivalences

Write an equivalent symbolization for each of the sentences in section 2 (4 pts each).

Symbolic Logic—PHI 210 C

Exam 3

Spring 2016 Section 6 (20 pts): Proofs in predicate logic

Symbolize the following argument (10 pts) and construct a proof (10 pts).

Be sure to justify every step in the proof!

1. All men must die.

2. Robert is a man.

3. Therefore, someone must die.