Free Printable logic

1.

Let A represent, "Elvis is alive," and let G represent, "Elvis gained weight." Translate the following symbols to English:

\sim\left(A\wedge G\right)

(a)

2.

Let A represent, "Elvis is alive," and let G represent, "Elvis gained weight." Translate the following symbols to English:

G\rightarrow\sim A

(a)

3.

If P represents, "I like Pepsi," and C represents, "I like Coke," which symbolic statement means, "I like Pepsi, and I do not like Coke"?

a)

$P\vee\sim C$

b)

$\sim P\wedge C$

c)

$P\wedge\sim C$

d)

$P\rightarrow\sim C$

e)

None of the Above

4.

If P represents, "I like Pepsi," and C represents, "I like Coke," which symbolic statement means, "I like Coke, or I like Pepsi"?

a)

$C\wedge P$

b)

$C\vee P$

c)

$C\rightarrow P$

d)

$\sim C\vee\sim P$

e)

None of the Above

5.

If P represents, "I like Pepsi," and C represents, "I like Coke," which symbolic statement means, "If I do not like Pepsi, then I like Coke"?

a)

$P\rightarrow C$

b)

$\sim P\rightarrow\sim C$

c)

$\sim P\vee C$

d)

$\sim P\rightarrow C$

e)

None of the above

6.

Write the following statement in symbolic notation: “I am going to watch a musical, and I will either laugh or cry.”

Let A = “I am going to watch a musical.”

Let B = “I will laugh.”

Let C = “I will cry.”

a)

$\left(A\wedge B\right)\vee C$

b)

$A\wedge B\vee C$

c)

$A\wedge\left(B\vee C\right)$

d)

None of the above

7.

"Either it shall rain or it shall not rain" is a

(a)

8.

The symbol ^ represents

a)

or

b)

negation

c)

and

d)

if.....then

9.

Which of the following means "not p or not q"

a)

~p v ~q

b)

p v q

c)

~p v q

d)

p v ~ q

10.

The symbol ^ represents

a)

or

b)

negation

c)

and

d)

if.....then

11.

Which of the following means "not p or not q"

a)

~p v ~q

b)

p v q

c)

~p v q

d)

p v ~ q

12.

The following statements represent p and q

p: the sea is calm

q: the sun is up

Which of the following means "the sea is calm or the sun is not up"

a)

p v ~q

b)

p ^ ~q

c)

p v q

d)

~p v ~q

13.

Which of the following is a contradiction of an A proposition?

a)

E

b)

I

c)

O

d)

None of the above

14.

"Either it shall rain or it shall not rain" is a

(a)

15.

Explain the term "Symbolic" in Symbolic Logic.

4 lines

16.

The symbol ^ represents

a)

or

b)

negation

c)

and

d)

if.....then

17.

Which of the following means "not p or not q"

a)

~p v ~q

b)

p v q

c)

~p v q

d)

p v ~ q

18.

The following statements represent p and q

p: the sea is calm

q: the sun is up

Which of the following means "the sea is calm or the sun is not up"

a)

p v ~q

b)

p ^ ~q

c)

p v q

d)

~p v ~q

19.

Which of the following is a contradiction of an A proposition?

a)

E

b)

I

c)

O

d)

None of the above

20.

"Either it shall rain or it shall not rain" is a

(a)

21.

Explain the term "Symbolic" in Symbolic Logic.

4 lines

22.

This symbol, ∧, means?

a)

and

b)

or

c)

not

d)

implies

23.

This symbol, ∨, means?

a)

and

b)

or

c)

not

d)

implies

24.

This symbol, ↔, means?

a)

and

b)

or

c)

if and only if

d)

implies

25.

p: It is raining.

q: The game is cancelled.

If it is raining, then the game is cancelled.

a)

$p\rightarrow q$

b)

$q\rightarrow p$

c)

$p\rightarrow\sim q$

d)

$\sim p\wedge q$

26.

p: It is raining.

q: The game is cancelled.

If it is not raining, then the game is cancelled.

a)

$p\rightarrow q$

b)

$q\rightarrow p$

c)

$\sim p\rightarrow q$

d)

$\sim p\wedge q$

27.

p: It is raining.

q: The game is cancelled.

It is not raining and the game is cancelled.

a)

$p\rightarrow q$

b)

$q\rightarrow p$

c)

$\sim p\rightarrow q$

d)

$\sim p\wedge q$

28.

p: It is raining.

q: The game is cancelled.

r: The boy is sad.

If it is raining and the game is cancelled, then the boy is sad.

a)

$p\rightarrow q\wedge r$

b)

$q\rightarrow p\vee r$

c)

$p\wedge q\rightarrow r$

d)

$\sim p\wedge q\vee r$

29.

p: It is raining.

q: The game is cancelled.

r: The boy is sad.

The game is cancelled and the boy is sad; therefore, it is raining.

a)

$q\wedge r\therefore p$

b)

$q\vee r\therefore p$

c)

$q\rightarrow r\wedge p$

d)

$q\wedge\sim r\rightarrow p$

30.

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

g\vee h

a)

If the girl runs, then the rabbit hops.

b)

The girl runs and the rabbit hops.

c)

The girl runs or the rabbit hops.

d)

If the rabbit hops, then the girl runs.

31.

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

g\wedge h\rightarrow j

a)

If the girl runs, then the rabbit hops and they are having fun.

b)

If the girl runs and the rabbit hops. then they are having fun,

c)

If the girl runs or the rabbit hops, then they are not having fun,

d)

If the rabbit hops, then the girl runs and they are having fun.

32.

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

j\therefore g\wedge h

a)

The girl and the rabbit are having fun if the girl runs and the rabbit hops.

b)

The girl runs and the rabbit hops. therefore, they are having fun,

c)

If the girl runs and the rabbit hops, then they are having fun,

d)

The girl and the rabbit are having fun, ,therefore, the girl runs and the rabbit hops.

33.

We use "if and only if " to talk about :

a)

conditional

b)

biconditional

c)

none of the options

34.

"The Tigers will play in the tournament if they win their next game." the Conclusion is:

a)

the Tigers win their next game

b)

they will play in the tournament

c)

none of the options

35.

"If two lines are perpendicular, then they intersect." the Conclusion is:

a)

two lines are perpendicular

b)

they intersect

c)

none of the options

36.

"A polygon is a rectangle if and only if it has four sides" is:

a)

conditional

b)

biconditional

c)

none of the options

37.

"Is a triangle if and only if the sum of the angles is 180° " is:

a)

conditional

b)

biconditional

c)

none of the options

38.

p: Sara likes physics.

q: Sara likes this book.

$p\rightarrow\sim q$ is:

a)

Sara likes physics, Sara not like this book.

b)

If Sara likes physics, then Sara like this book.

c)

none of the options

39.

p: Sara likes physics.

q: Sara likes this book.

$p\rightarrow\sim\left(\sim q\right)$ is:

a)

Sara likes physics, Sara not like this book.

b)

If Sara likes physics, then Sara likes this book.

c)

none of the options

40.

$p\leftrightarrow q$

a)

conditional

b)

biconditional

c)

none of the options

41.

$T\leftrightarrow F$

a)

F

b)

T

c)

none of the options

42.

"If points A, B, and C lie on line l , then they are collinear." the hypothesis is:

a)

points A, B, and C lie on line l

b)

they are collinear

c)

none of the options

43.

Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.

a)

Law of Detachment

b)

Law of Contrapositive

c)

Law of Syllogism

d)

Law of Biconditional

44.

What is the conclusion made using syllogism: If it rains on my bike, then it will get rusty.
If it gets rusty, then I can't ride it anymore.

a)

If it rains on my bike, then I can ride it.

b)

If it gets rusty, then I can't ride it.

c)

If it rains on my bike, then I can't ride it anymore.

d)

None of the above

45.

For the inverse we _________ the hypothesis and conclusion

a)

switch

b)

negate

c)

switch and negate

46.

For the contrapositive we _________ the hypothesis and conclusion

a)

switch

b)

negate

c)

switch and negate

47.

This symbol, ∧, means?

a)

and

b)

or

c)

not

d)

implies

48.

This symbol, ∨, means?

a)

and

b)

or

c)

not

d)

implies

49.

This symbol, ↔, means?

a)

and

b)

or

c)

if and only if

d)

implies

50.

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3) ???????
What belongs in line 3?

a)

Figure A is a polygon.

b)

Figure A is a circle.

c)

Figure A is a square.

d)

invalid; nothing belongs in line 3

51.

All bears are mammals, all mammals have kidneys; therefore all bears have kidneys.

a)

Deductive

b)

Inductive

52.

Sarah just moved here from Chicago, and she has blue eyes. Therefore, all people from Chicago have blue eyes.

a)

Deductive

b)

Inductive

53.

All numbers ending in 0 or 5 are divisible by 5. The number 35 ends with a 5, so it is divisible by 5.

a)

Deductive

b)

Inductive

54.

It is dangerous to drive on icy streets. The streets are icy now so it is dangerous to drive now.

a)

Deductive

b)

Inductive

55.

All basketball players in your school are tall, so all basketball players must be tall.

a)

Deductive

b)

Inductive

56.

Which statement is the converse of the given statement?
If you make an insurance claim, then your rates will go up.

a)

If your insurance rates do not go up , then you have not maid a claim.

b)

If you do not make an insurance claim, then your rates will not go up.

c)

If your insurance rates go up, then you have made an insurance claim.

d)

If you make an insurance claim, then your rates will not go up.

57.

Let p represent: Brent works this summer.
Let q represent: Brent takes a vacation.
What is the symbolic representation of this statement?
Therefore, Brent does not work this summer.

a)

∴~p

b)

∴~q

c)

~p

d)

~q

58.

Let V represent Vehicles. Let M represent motorized vehicles, and let A represent automobiles.
Which is not a valid conclusion?

a)

Not all motorized vehicles are automobiles.

b)

Not all automobiles are motorized vehicles

c)

Some motorized vehicles are not automobiles.

d)

Automobiles are motorized vehicles.

59.

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

a)

If I do not have a Siberian Husky, then I do not have a dog.

b)

If I have a dog, then I have a Siberian Husky.

c)

If I do not have a dog, then I do not have a Siberian Husky.

d)

If I do not have a Siberian Husky, then I have a dog.

60.

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

a)

If I do not have a Siberian Husky, then I do not have a dog.

b)

If I have a dog, then I have a Siberian Husky.

c)

If I do not have a dog, then I do not have a Siberian Husky.

d)

If I do not have a Siberian Husky, then I have a dog.

logic

Total questions: 60

Worksheet time: 3600secs

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