Free Printable Propositional Logic

1.

Every propositions has a truth value

a)

True

b)

False

2.

Which one are propositions?

a)

3*2 = 5

b)

He is the most handsome man.

c)

You should get vaccine for COVID-19

d)

There was snow in Khon Kaen yesterday.

e)

2 is an odd number.

3.

"Who is he?" is a proposition.

a)

True

b)

False

4.

Two atomioc propositions joined by a connective to form a compound statement are known as a disjunction.

a)

True

b)

False

5.

A double negation is the same thing as no negation.

a)

True

b)

False

6.

The conditional statement $p\ \rightarrow\ q$ is false only when p is true and q is false.

a)

True

b)

False

7.

How many rows in a truth table for a proposition with 3 atomic proposition.

a)

3

b)

4

c)

8

d)

10

8.

What is the proposition of the following statement : "If tomorow is sunday then there will be no rain". Define p as "tomorrow is sunday", q as "there will be rain".

a)

$p\rightarrow q$

b)

$p\vee q$

c)

$p\wedge q$

d)

$p\leftrightarrow q$

9.

What is the proposition of the following statement: "Mark is a math major and Mark’s sister is a computer science major.". Define p as "Mark is a math major", and q as "Mark's sister is a computer science major".

a)

$p\rightarrow q$

b)

$p\vee q$

c)

$p\wedge q$

d)

$p\leftrightarrow q$

10.

What is the proposition of the following statement : "Mark is a math major or Mark’s sister is a computer science major.". Define p as "Mark is a math major", and q as "Mark's is a computer science major".

a)

$p\rightarrow q$

b)

$p\vee q$

c)

$p\wedge q$

d)

$p\leftrightarrow q$

11.

Which are corrects on logically equivalent?

a)

$\left(p\wedge q\right)\wedge r\ \equiv p\wedge\left(q\wedge r\right)$

b)

$p\wedge T\equiv p$

c)

$p\wedge\sim p\equiv c$

d)

$\sim\left(p\wedge q\right)\equiv\sim p\vee\sim q$

12.

Which are tautologies?

a)

$p\rightarrow p$

b)

$p\wedge\sim p$

c)

$p\leftrightarrow\left(p\wedge p\right)$

d)

$p\vee T$

13.

Which are contradictions?

a)

$p\wedge\sim p$

b)

$p\wedge c$

c)

$p\vee\sim p$

d)

$c\rightarrow p$

14.

What are true about the argument?

a)

An argument is a sequence of propositions

b)

Each proposition before the final one is called premise

c)

The final proposition is called the conclusion

d)

an argument is valid if all premises are true then the conclusion is true.

15.

How do you validate an argument?

a)

Using truth table

b)

Using the rules of inference

c)

Using logical equivalence

d)

Using set theory

16.

When the argument is valid which one of these statement are true?

a)

In the truth table, all conclusions are true for every critical rows.

b)

Some of the premises can be false.

c)

The conclusion is true using the rule of inference.

d)

In the truth table, some of the premises are false.

17.

Let d be “Discrete Math is difficult,” f be "Discrete Math is fun,” and n be “Disceret Math is necessary.”. Using the symbols what is the statement for "Disceret Math is fun, but it is not both difficult and necessary.

a)

f∧∼(d∧n)

b)

f∧d∧n

c)

f∧∼d∧n

d)

f∧∼d∧∼n

18.

Let p be “x > 2,” q be “x = 2,” and r be “x > 5”. Using the defined symbols, what is the statement 2 <= x <= 5.

a)

(p∨q)∧∼r

b)

(p∨q)∧r

c)

(p∧q)∧∼r

d)

∼(p∨q)∧r

19.

What is a contrapositive of the following statement "If the world is ending tomorrow then I will not go to school"

a)

If I go to school then the world is not ending tomorrow.

b)

If I do not go to school then the world is ending tomorrow.

c)

If the world is not ending tomorrow then I will go to school

d)

If I do not go to school then the world is not ending tomorrow.

20.

What is the negation of the following statement? "If a butterfly lays eggs then there will be more butterfiles".

a)

A butterfly lays eggs and there is no more butterflies.

b)

If a butterfly lays egg then these is no more butterflies

c)

If a butterfly does not lay egg then there is no more butterflies.

d)

If a butterfly does not lay egg then there is more butterflies

21.

Which of the following are tautology?

a)

p→(q∨r)≡(p∧∼q)⟶r

b)

p∧∼p

c)

(p∧q)∨(∼p∨(p∧∼q))

d)

(p∧∼q)∧(∼p∨q)

e)

(p→r)↔(q→r)

22.

Which of the following are contradiction ?

a)

p→(q∨r)≡(p∧∼q)⟶r

b)

p∧∼p

c)

(p∧q)∨(∼p∨(p∧∼q))

d)

(p∧∼q)∧(∼p∨q)

e)

(p→r)↔(q→r)

23.

Which of the following statements are true?

a)

An argument is a sequence of propositions

b)

Each proposition before the final one is called conclusion

c)

The final proposition is called the premise

d)

The argument is valid if assuming all the premises are true then the conclusion is true.

e)

To validate an argument, we assume no premises are true.

24.

If Ironman is a man, then Ironman is mortal

Ironman is a man

∴ Ironman is mortal

This argument is valid because of which rule of inference?

a)

Modus ponens

b)

Modus tollens

c)

Hypothetical syllogism

d)

Disjunctive syllogism

25.

What should be put in on the red line?

a)

Premise

b)

Modus Ponens

c)

Modus Tollens

d)

Disjunctive syllogism

e)

Dilemma proof

26.

Which logical expression give the truth values as shown in trught table?

a)

p∧q

b)

p V q

c)

p→q

d)

~p

e)

p↔q

27.

Which one of the following expression are well-formed formula?

a)

p V q

b)

p→→q

c)

p V V q

d)

q ⟷ q

e)

∼∼p→∼q

28.

Which expression give you the following truth values in a truth table?

a)

p→q

b)

q→(p∧r)

c)

p→(q∨∼r)

d)

q V ~r

29.

Consider the following argument:

$p\ \rightarrow\ q$

$q\ \rightarrow\ p$

$\therefore p\ \wedge\ q$

Which statements are true?

(a)

Choose from the below words

The argument is valid.

The argument is invalid.

The argument is not complete.

The argument cannot be conluded.

30.

Consider the following argument:

$p$

$p\ \rightarrow\ q$

$\sim q\vee\ r$

$\therefore r$

The argument is (a)

Choose from the below words

not valid

valid.

neither valid on invalid.

in not complete.

Propositional Logic

Total questions: 30

Worksheet time: 42mins

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