Section I: True / False questions (4 points each)

[Pages:6]PHIL 240, Introduction to Logic, Sections 512-520 FINAL EXAM ? Practice

Fall 2011

Name (5 points): _________________________________ Section (5 points): _______

Section I True / False questions (2 points each)

1. __________ Any argument that is sound is also valid. 2. __________ If the premises of an argument are all true, then that argument is

sound. 3. __________ Every universal wff contains at least one variable. 4. __________ Some wffs contain free variables. 5. __________ If the conclusion of a valid argument is false, then its premises must

all be false. 6. __________ Every argument in sentential logic has an invalidating assignment. 7. __________ Every wff of predicate logic contains at least one quantifier. 8. __________ Some conditionals are atomic wffs. 9. __________ Every argument has at least two premises. 10. __________ Every WFF that starts with the symbol x is an existential.

Section II Mark the correct completion (5 points each)

1. The conclusion of a valid argument ...

(a) _____ must be false if the premises are all false.

(b) _____ must be true if the premises are all true.

(c) _____ must be false if all the premises are true.

(d) _____ must be true if all the premises are false.

(e) _____ must be true if it is also false.

2. The following is NOT a condition on the application of E ...

(a) _____ the instantial name must occur in the line which is repeated.

(b) _____ the instantial name cannot occur in the line containing the sentence which is repeated.

(c) _____ the instantial name cannot occur in the line that motivates the assumption to be discharged.

(d) _____ the instantial name cannot occur in the assumption set of the line containing the sentence which is repeated save for the assumption itself.

PHIL 240, Introduction to Logic, Sections 512-520 FINAL EXAM ? Practice

Fall 2011

Name (5 points): _________________________________ Section (5 points): _______ 3. A finite interpretation may contain all but ...

(a) _____ a universe (b) _____ predicate extensions (c) _____ truth value specifications (d) _____ a galaxy

4. The condition on I requires that ...

(a) _____ the instantial name must occur in at least one of the sentences in the assumption of the line to which one applies the rule.

(b) _____ there is no condition on the application of I.

(c) _____ the instantial name cannot occur in any sentence in the assumption set of the line to which one applies the rule.

(d) _____ a free variable must be used in place of an instantial name.

(e) _____ the instantial name be used in the sentence which results from the application of the rule.

5. (A (B & ~C)) is a ...

(a) _____ conditional (b) _____ conjunction (c) _____ negation (d) _____ disjunction (e) _____ not a WFF

PHIL 240, Introduction to Logic, Sections 512-520 FINAL EXAM ? Practice

Fall 2011

Name (5 points): _________________________________ Section (5 points): _______

Section III Translations (5 points each)

Using the following translation scheme, construct a strictly correct translations that includes all parentheses.

Bx = `x is a book'

Hx = `x is a hardback'

Px = `x is a paperback'

P = Peter Dances

Q = Jane Dances

1) Peter dances if and only if Jane Dances.

2) All books are paperbacks.

3) All books are either hardback or paperback.

PHIL 240, Introduction to Logic, Sections 512-520 FINAL EXAM ? Practice

Fall 2011

Name (5 points): _________________________________ Section (5 points): _______ Section IV Proofs (5 points each) Give a proof for each of the following sequents. You may use both primitive and derived rules.

1. x(Fx Gx), x(Gx Hx), xFx xHx

2. (P R), (~R v Q), (Q S) (P S)

PHIL 240, Introduction to Logic, Sections 512-520 FINAL EXAM ? Practice

Fall 2011

Name (5 points): _________________________________ Section (5 points): _______

3. x(Dx Ax), x(Ax Cx), xDx xCx

PHIL 240, Introduction to Logic, Sections 512-520 FINAL EXAM ? Practice

Fall 2011

Name (5 points): _________________________________ Section (5 points): _______

Section V Truth Tables (5 points each)

Answer each question using truth tables. You may use either direct or indirect truth tables, but if you choose to use an indirect truth table, sufficient work must be shown to indicate how you reached your answer.

(P ~Q) ~(P Q)

Section IV Finite Interpretations (2 points each)

For each of the sentences below, indicate whether it is true or false in this finite interpretation:

U: {a, b, c} F: {a} G: {a, b, c} L: {, , , }

1. ________ 2. ________ 3. ________ 4. ________

5. ______

xyLxy x(Fx & Gx) (xGx xFx) xLxx xGx

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