Free Printable Logic test 1

1.

Valid Arguement:

a)

An argument where it is impossible for the premises to be true and the conclusion false

b)

a valid argument with true premises

c)

a sentence which is true in every row of a truth table

d)

true in all possible ways

2.

Sound Argument

a)

an argument where it is impossible for the premises to be true and the conclusion falls

b)

a valid argument with true premises

c)

true in all possible worlds

d)

an argument where two sentences are tautologically equivalent when the truth tables for the statements are identical

3.

The following is an example of...

P1 Jackie's baby is a turtle or a frog

P2 Jackies baby is not a frog

C. Jackies baby is a turtle.

a)

Valid Argument

b)

Sound Argument

4.

The following is an example of...

P1 Jackies baby is a girl or boy

P2 Jackies baby is not a boy

C Jackies baby is a girl.

a)

Sound Argument

b)

Valid Argument

5.

Logical Truth:

a)

true in all possible worlds

b)

must always be true

c)

a sentence which is true in every row of a truth table

6.

Logical Necessity:

a)

could be true

b)

Must always be true

c)

when the truth tables for the statements are identical

7.

logical possibility:

a)

could be true

b)

logical possibility is not a physical possibility

c)

logical possibility is a physical possibility

8.

tautology:

a)

a sentence which is true in every row of a truth table

b)

A statement that is always true.

c)

A statement that is always false.

d)

the truth tables for the statements are identical

9.

Tautological Equivalence:

a)

when the truth tables for the statements are identical

b)

Q is equivalent of P if when P is true, Q is always true as well

c)

a sentence which is true in every row of a truth table

10.

Tautological Consequence:

a)

Q is a tautological consequence of P if when P is true, Q is always true as well

b)

Q is a tautological consequence of P if when P is true, Q is false

c)

P is a tautological consequence of Q if when Q is true, P is always true as well

d)

Q is not a tautological consequence of P if when P is true, Q is always true as well

11.

negation, ¬:

(a)

12.

Conjunction, ∧

(a)

13.

Disjunction ∨

(a)

14.

Simplification:

Associativity of ∧

a)

P ^( Q ^ R) <=> (P ^Q) ^R

<=> P ^ Q ^ R

b)

P ^ Q <=> Q ^ P

c)

P^P <=> P

15.

Simplification:

Associativity of v:

a)

P v (Q v R) <=> (P v Q) v R

<=> P v Q v R

b)

P v Q <=> Q v P

c)

P v P <=> P

16.

Simplification:

Commutativity of ^:

a)

P ^(Q ^ R) <=> ^ R

<=> P ^ Q ^ R

b)

P ^ Q <=> Q ^ P

c)

P ^ P <=> P

17.

Simplification:

Commutativity of v:

a)

P v( Q vR) <=> (P v Q) v R

<=> P v Q v R

b)

P v Q <=> Q v P

c)

P v P <=> P

18.

Simplification:

Idempotence of ^

a)

P ^ (Q ^ R) <=> (P ^ Q) ^ R

<=> P ^ Q ^ R

b)

P ^ Q <=> Q ^ P

c)

P ^ P <=> P

19.

Simplification:

Idempotence of V

a)

P v( Q v R) <=> (P v Q) v R

<=> P v Q v R

b)

P v Q <=> Q v P

c)

P v P <=> P

20.

Negation Normal Form/NNF

a)

¬(¬(¬A ∧ B) ∧ C) <=> ¬(( ¬¬A∧¬B)∧C)

<=> ((A ∧¬B)∧ C)

<=> ¬(A∧¬B)∨ ¬C

<=> (¬A ∨ B) ∨ ¬C

b)

¬(¬(¬A ∧ B) ∨ C) <=> ¬(( ¬¬A∧¬B)∧C)

<=> ((A ∧¬B)∧ C)

<=> ¬(A∨¬B)∨ ¬C

<=> (¬A ∨ B) ∨ ¬C

21.

De Morgans Laws:

a)

¬¬ P <=> P

b)

¬ ( P ∧ Q) <=> (¬P ∨¬Q)

c)

¬(P∨Q) <=> (¬P ∧¬Q)

d)

¬¬P ∨ Q <=> P∧Q

22.

Identity Elimination ( =Elim_

a)

P(n)

:

n=m

:

>P(m)

b)

n=n

c)

Pi

:

P1 v... Pi v...v Pn

23.

Identity Introduction ( = Intro)

a)

n=n

b)

P

:

P

24.

Disjunction Introduction ( V Intro)

a)

Pi

:

P1 v... Pi v... v Pn

b)

P1

∇

Pn

:

P1 ^... ^ Pn

c)

P1 ∧...∧ Pi ∧...∧Pn

:

Pi

25.

Conjunction Introduction ( ∧ Intro)

a)

Pi

:

P1∨... Pi

b)

P1

⊽

Pn

:

P1 ∧...∧Pn

c)

P1 ∨...∨Pn

P1

:

s

Pn

:

s

:

s

26.

Disjunction Elimination ( v Elim)

a)

P1 ∨...∨Pn

P1

:

s

Pn

:

s

:

s

b)

P1

V

Pn

:

P1 ^... ^Pn

c)

Pi

:

P1 v... Pi v....vPn

27.

Conjunction Eliminations ( ^ Elim)

a)

P1 ∨...∨Pn

P1

:

s

Pn

:

s

:

s

b)

P1 ∧...∧Pi∧... ∧Pn

:

Pi

c)

Pi

:

P1 ∨... Pi ∨... ∨ Pn

Logic test 1

Total questions: 27

Worksheet time: 16mins

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