Introduction to Formal Logic – Predicate Logic Examination – Fall 2017 Part I: T

Question

Introduction to Formal Logic – Predicate Logic Examination – Fall 2017

Part I: True/False

Instructions. Please circle ‘True ‘if the statement is true and ‘False’ if the statement is false. (3 pts)

1. The symbol used to capture the idea that universal statements assert something about every member of the subject class is the existential quantifier.

A) True                        B) False

2. The domain of discourse is the set of individuals over which a quantifier ranges.

A) True                        B) False

3. A substitution instance of a statement function can be validly deduced from the universally quantified statement by the rule of universal instantiation (UI).

A) True                        B) False

4. Bound variables are variables that are not governed by any quantifier.

A) True                        B) False

5. The change of quantifier rule allows the removal or introduction of conditional statements.

A) True                        B) False

Part II: Translation

Instructions. Please translate the following statements into symbolic predicate notation. (3 pts)

6. No music videos are violent.

7. Turner Classic Movies is the best source for film noir.

8. If anything is a breakfast cereal, then it is full of vitamins.

9. A human is alive if and only if there is brain activity.

10. Some green fruits are not sweet.

Part III: Rules of Implication

Instructions. Please prove the following arguments valid using the rules of instantiation, generalization, instantiation, and Change of Quantifier. (10 pts)

11.          1. (x)Px É (x)(Rx É ~ Lx)

               2. (x) (Rx É ~ Lx) É Ta

               3. Ta É (x)Sx                     /~(x)Px v (x)Sx

12.      1. ~ Kc · Hc

          2. (x)[Hx É (Kx v Lx)]                   / Lc

13.      1. (x) (~ Hx · Kx)

          2. (x)(Kx É (Lx v Hx)                                 / (x) Lx

14.       1. (x) Dx É (x) Cx

          2. Dc v ~ Ex

          3. ~ (x) Cx                                          / ~ (x) Ex

Part IV: Conditional/Indirect

Instructions. Using either an indirect or conditional proof, please solve the following. (10pts)

15.        1.       (x) ~ Ex

          2. ~ (x) Cx É (x) (Dx · Ex)                  / (x) Cx        

Part III: Proving Invalidity

Instructions. Please use the finite universe method to prove the following argument invalid. (10 pts)

16.                   1. (x) ~Px

                  2. (x) (Sx É Px)                          / (y) (Sy Py)

Part IV: Translation

Instructions. Please translate and prove the following argument valid in symbolic predicate notation (10 pts)

17.       All professional basketball players are paid to play basketball. Some professional basketball players are short. Therefore, some short basketball players are paid. (B, P, S)

Explanation / Answer

1. False

The symbol used to capture the idea that universal statements assert something about every member of the subject class is the universal quantifier.

2. True

3. True

4. False

Variables governed by a quantifier are called bound variables.

5. False

Change of quantifier rule: Allows the removal or introduction of negation signs.

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