Free Printable LOGIC QUIZ NO.1

Worksheets

LOGIC QUIZ NO.1

Total questions: 50

Worksheet time: 2hrs 40mins

Name

Class

Date

All dogs are poddles.

True

False

What symbol represents a conjunction?

$\vee$

$\wedge$

$\perp$

$\sim$

What symbol represents a disjunction?

$\vee$

$\wedge$

$\perp$

$\cong$

Two statements connected by the word "and" is

A disjunction

A conjunction

A conjunction is true only if

Both statements are false

Both statements are true

One statement is true

One statement is false

A disjunction is true if

Both statements are false

Only one statement is true

At least one statement is true

Negate the statement:

"I love Geometry"

Geometry I love

If I love Geometry, then I do not love Geometry

If and only if I love Geometry

I do not love Geometry

This symbol, ∨, means?

and

not

implies

Determine the truth values of the following compound statements.

$7$ is a factor of $21$ and $84$

True

False

10.

Determine the truth values of the following compound statements.

February or October has $30$ days.

True

False

11.

Determine the truth values of the following compound statements.

$15+7<27$ and $2×8=28$

True

False

12.

Determine the truth values of the following compound statements.

$27$ is a multiple of $7$ or $\left(-2\right)^2<0$

True

False

13.

Determine the truth values of the following compound statements.

$49$ is a perfect square or a prime number

True

False

14.

Determine the truth values of the following compound statements.

$2$ minutes = $120$ seconds and $2$ hours = $12$ minutes

True

False

15.

Let p and q represent the following simple statements;

p: Frank plays football.

q: Jamir runs track.

r: Edwin plays soccer.

Write each compound statements in symbolic form.

Frank plays football and Jamir runs track.

p→q

p↔q

p Λ q

p v q

16.

Let p and q represent the following simple statements;

p: Frank plays football.

q: Jamir runs track.

r: Edwin plays soccer.

Write each compound statements in symbolic form.

Edwin plays soccer or Frank does not play football.

$r\longrightarrow\sim p$

$r\vee\sim p$

$r\wedge\sim p$

$r\longleftrightarrow\sim p$

17.

Used to prove that a conjecture is false.

Counterexample

Inductive Reasoning

Concluding statement

Conjecture

18.

What is the symbol for NOT (negation)?

∕

∨

∧

19.

What are the next 2 numbers of this pattern?
23, 27, 31, 35, ___, ___

37, 39

40, 45

39, 43

38, 41

20.

Which statement has a true truth value?

Fish can walk

Chicken has four legs.

Birds can fly.

Shark has two legs.

21.

What is the truth value for the statement below?

2x+1=3, given x=1

True

False

22.

In a disjunction, even if one of the statements is false, the whole disjunction is still...

False

Both true and false

True

Negated

23.

In a truth table for a two-variable argument, the first guide column has the following truth values:

F, F, T, T

T, F, T, F

T, F, F, F

T, T, F, F

24.

The four logical connectives are…

Conjunctions, conditionals, compounds, and disjunctions

Conjunctions, statements, disjuncts, and conditionals

Conditionals, disjunctions, negations, and conjunctions

Conjuncts, statements, conditionals, and negations

25.

A conditional is false only when the hypothesis is…

True and the conclusion is false

False and the conclusion is false

True and the conclusion is true

False and the consequent is true

26.

Find the truth value of given statement : 4+3=9

False

True

27.

Which of the following option is true?

If the Sun is a planet, elephants will fly

if 5-2 = 7, then 3 +2 = 8

1 > 3 and 3 is a positive integer

2 > 3 or 3 is a negative integer

28.

p: The girl wears a red hat.
q: The boy wears a blue coat.
Which of the following statements is equivalent to

p\wedge q

The girl wears a red hat and the boy wears a blue coat.

The girl wears a red hat or the boy wears a blue coat.

If the girl wears a red hat, then the boy wears a blue coat.

The boy wears a blue coat if and only if the girl wears a red hat.

29.

Given:
p: It snows on Sunday.
q: It rains on Saturday.

Which of the following states:

p\therefore q

It snows on Sunday, therefore it rains on Saturday.

It snows on Sunday or it rains on Saturday.

If it snows on Sunday, then it rains on Saturday.

It rains on Sunday or it snows on Saturday.

30.

Given:
p: It will rain on Saturday.
q: We will play in the park.

Write the following statement using logic symbols.
If it does not rain on Saturday, then we will play in the park.

$\sim p\rightarrow q$

$p\rightarrow q$

$\sim p\wedge q$

$\sim q\rightarrow p$

31.

Given:
p: Juan eats apples.
q: Juan drinks juice.

Write the following:

p\vee\sim q

Juan eats apples or Juan does not drink juice.

Juan eats apples and Juan drinks juice.

If Juan eats apples, then Juan does not drink juice.

Juan does not eat apples or drink juice.

32.

Given:
p: Six students eat candy.
q: It rains on Tuesday.

Which of the following states:

\sim q\rightarrow\sim p

If it does not rain on Tuesday, then six students will not eat candy.

If six students do not eat candy, then it does not rain on Tuesday.

Six students do not eat candy, and it does not rain on Tuesday.

It does not rain on Tuesday or six students will not eat candy.

33.

Given:

p: Victor gets paid on Friday.

q: Victor eats Tacos for dinner.

r: Victor goes to the game.

Write the following in logic symbols:

If Victor eats tacos for dinner, then he does not go to the game.

$q\rightarrow\sim r$

$p\rightarrow\sim q$

$p\rightarrow\sim r$

$q\vee\sim r$

34.

Given:
p: Emma wears a green dress.
q: Maria wears a pink dress.
r: Vera wears a blue dress.

Which states:

\left(p\wedge r\right)\rightarrow q

If Emma wears a green dress and Vera wears a blue dress, then Maria wears a pink dress.

If Emma wears a green dress then Maria wears a pink dress.

If Emma wears a green dress, then Vera wears a blue dress and Maria wears a pink dress.

Emma wears a green dress and Vera wears a blue dress and Maria wears a pink dress.

35.

Given:

p: Arturo paints.

q: David draws.

r: Marcus sculpts.

Write in logic symbols: If Marcus sculpts, then Arturo paints or David does not draw.

$r\rightarrow\left(p\vee\sim q\right)$

$r\rightarrow\left(p\wedge\sim q\right)$

$p\rightarrow\left(q\vee\sim r\right)$

$r\wedge p\wedge\sim q$

36.

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

I do not have three cats.

¬ p

¬ q

^ p

^ q

37.

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

If I have three cats, then I am insane.

q => p

p => q

p v q

p ^ q

38.

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

If I am not insane, then I do not have three cats.

¬ q => p

¬ p => q

¬ q => ¬ p

¬ p => ¬ q

39.

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

I have three cats if and only if I am insane.

q => p

p => q

q <=> p

p <=> q

40.

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

If I am insane, then I have three cats.

q => p

p => q

q <=> p

p <=> q

41.

Given the statement, "If I have three cats, then I am insane”, write the converse of the statement.

If I have three cats, then I am insane.

If I am not insane, then I do not have three cats.

If I am insane, then I have three cats.

If I do not have three cats, then I am not insane.

42.

Given the statement, "If I have three cats, then I am insane”, write the inverse of the statement.

If I have three cats, then I am insane.

If I am not insane, then I do not have three cats.

If I am insane, then I have three cats.

If I do not have three cats, then I am not insane.

43.

Given the statement, "If I have three cats, then I am insane”, write the contrapositive of the statement.

If I have three cats, then I am insane.

If I am not insane, then I do not have three cats.

If I am insane, then I have three cats.

If I do not have three cats, then I am not insane.

44.

Which statement is logically equivalent to p => q ?

¬ p => ¬ q

¬ q => ¬ p

q => p

45.

State whether the argument below is valid or invalid. If it is invalid, give a reason why it is invalid.

If Joe eats greasy food, he will feel sick.

Joe does not eat greasy food.

Therefore, Joe won’t feel sick.

valid

invalid, inverse error

invalid, converse error

46.

State whether the argument below is valid or invalid. If it is invalid, give a reason why it is invalid.

If Joe eats greasy food, he will feel sick.

Joe feels sick.

Therefore, Joe ate greasy food.

valid

invalid, inverse error

invalid, converse error

47.

State whether the argument below is valid or invalid. If it is invalid, give a reason why it is invalid.

All weebles are wobbles.

All wobbles have woozles.

Therefore, all weebles have woozles.

valid

invalid; because weebles, wobbles, and woozles do not exist

invalid; because the conclusion does not follow logically from the premises

48.

Classify the valid argument below as sound or unsound. If it is unsound, give a reason why it is unsound.

If a person is caring, he will help when others are in need.

Antoine didn't help when others were in need.

Therefore, Antoine isn't caring.

sound

unsound; the first premise (first sentence) is faulty

unsound; the second premise (second sentence) is faulty

49.

Classify the valid argument below as sound or unsound. If it is unsound, give a reason why it is unsound.

2 + 2 = 4.

4 + 5 = 9.

Therefore, 2 + 2 + 5 = 9.

sound

unsound; the first premise (first sentence) is faulty

unsound; the second premise (second sentence) is faulty

50.

Check all of the following that are logical "statements":

I love this song!

3 + 5 = 8

School was canceled yesterday.

Where did he come from?

Be careful what you wish for.

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LOGIC QUIZ NO.1

Total questions: 50

Worksheet time: 2hrs 40mins

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