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Logic Questions

Total questions: 76

Worksheet time: 38mins

Name
Class
Date
1.

What is a statement in logic?

a)

A question that requires an answer

b)

A sentence that is either true or false

c)

A command to perform an action

d)

A sentence with no meaning

2.

Which of the following is not a statement?

a)

The sun rises in the east.

b)

Is it raining outside?

c)

5 + 3 = 8

d)

The triangle has three sides.

3.

What is the truth value of a true statement in logic?

a)

False

b)

True

c)

Undetermined

d)

None

4.

What is the truth value of the statement “2 + 2 = 22”?

a)

True

b)

False

c)

Sometimes true

d)

Cannot be determined

5.

Which of the following is a compound statement?

a)

The sky is blue.

b)

It is raining and cold.

c)

A square has four sides.

d)

7 is a prime number.

6.

What is the negation of the statement “It is sunny”?

a)

It is not sunny.

b)

It is raining.

c)

It is cloudy.

d)

It is warm.

7.

If a statement is false, what is the truth value of its negation?

a)

True

b)

False

c)

Undetermined

d)

None

8.

What is the negation of “All students passed the exam”?

a)

Some students passed the exam.

b)

Some students did not pass the exam.

c)

All students failed the exam.

d)

No students passed the exam.

9.

In logic, what is a proposition?

a)

A question

b)

A statement with a truth value

c)

A suggestion

d)

A hypothesis

10.

What is the truth value of “The Philippines is an archipelago”?

a)

True

b)

False

c)

Sometimes true

d)

Cannot be determined

11.

Which of the following is a simple statement?

a)

I will study or sleep.

b)

The room is bright.

c)

If it rains, then I stay home.

d)

The number is even and positive.

12.

Is the statement “3 is an odd number” true?

a)

True

b)

False

c)

Undetermined

d)

None

13.

What is the negation of “The number is even”?

a)

The number is odd.

b)

The number is not even.

c)

The number is positive.

d)

Both a and b

14.

Which of the following is a declarative sentence?

a)

Close the door.

b)

What time is it?

c)

The earth is round.

d)

Run fast!

15.

In logic, what does “p” typically represent?

a)

A variable

b)

A proposition

c)

A number

d)

A function

16.

Is the statement “All triangles have three sides” true?

a)

True

b)

False

c)

Sometimes true

d)

Cannot be determined

17.

What is the truth value of “A rectangle has five sides”?

a)

True

b)

False

c)

Undetermined

d)

None

18.

Which of the following is a compound proposition?

a)

The day is Monday.

b)

It is hot or humid.

c)

4 is a prime number.

d)

The circle is round.

19.

What is the negation of “Some dogs bark”?

a)

Some dogs do not bark.

b)

All dogs bark.

c)

No dogs bark.

d)

Some dogs are quiet.

20.

What is the truth value of “1 + 1 = 11”?

a)

True

b)

False

c)

Sometimes true

d)

Cannot be determined

21.

In logic, what is a statement that is always true called?

a)

A contradiction

b)

A tautology

c)

A fallacy

d)

A paradox

22.

Which of the following is a tautology?

a)

It is raining or it is not raining.

b)

It is raining and it is not raining.

c)

If it rains, then it is sunny.

d)

The number is even and odd.

23.

What is a statement that is always false called?

a)

A tautology

b)

A contradiction

c)

A proposition

d)

A conditional

24.

Which of the following is a contradiction?

a)

The number is positive or negative.

b)

The number is even and odd.

c)

The sky is blue or green.

d)

It is day or night.

25.

What is the truth value of “All squares are rectangles”?

a)

True

b)

False

c)

Sometimes true

d)

Cannot be determined

26.

Which symbol represents the logical connective “AND”?

a)

b)

c)

d)

27.

When is the truth value of p ∧ q true?

a)

Both p and q are true

b)

Either p or q is true

c)

Both p and q are false

d)

p is true and q is false

28.

Which symbol represents the logical connective “OR”?

a)

b)

c)

d)

¬

29.

When is the truth value of p ∨ q false?

a)

Both p and q are true

b)

Both p and q are false

c)

p is true and q is false

d)

p is false and q is true

30.

If p is true, what is the truth value of ¬p?

a)

True

b)

False

c)

Undetermined

d)

None

31.

In the statement “p → q,” what is p called?

a)

Conclusion

b)

Hypothesis

c)

Converse

d)

Inverse

32.

In the conditional statement “If it rains, then I stay home,” what is the conclusion?

a)

It rains

b)

I stay home

c)

It does not rain

d)

I go out

33.

What is the truth value of p → q when p is false?

a)

True

b)

False

c)

Depends on q

d)

Undetermined

34.

What is the converse of “If p, then q”?

a)

If q, then p

b)

If not p, then not q

c)

If not q, then not p

d)

If p, then not q

35.

What is the converse of “If it is Monday, then I have class”?

a)

If I have class, then it is Monday.

b)

If it is not Monday, then I have no class.

c)

If I have no class, then it is not Monday.

d)

If it is Monday, then I have no class.

36.

What is the inverse of “If p, then q”?

a)

If not p, then not q

b)

If q, then p

c)

If not q, then not p

d)

If p, then not q

37.

What is the inverse of “If it is sunny, then I go to the park”?

a)

If it is not sunny, then I do not go to the park.

b)

If I go to the park, then it is sunny.

c)

If I do not go to the park, then it is not sunny.

d)

If it is sunny, then I do not go to the park.

38.

What is the contrapositive of “If p, then q”?

4 lines
39.

What is the contrapositive of “If p, then q”?

a)

If not q, then not p

b)

If q, then p

c)

If not p, then not q

d)

If p, then not q

40.

What is the contrapositive of “If I study, then I pass”?

a)

If I do not pass, then I did not study.

b)

If I pass, then I study.

c)

If I do not study, then I do not pass.

d)

If I study, then I do not pass.

41.

Which logical connective is used in “It is raining and it is cold”?

a)

OR

b)

AND

c)

NOT

d)

IMPLIES

42.

What is the truth value of ¬(p ∧ q) equivalent to?

a)

¬p ∨ ¬q

b)

¬p ∧ ¬q

c)

p ∨ q

d)

p ∧ q

43.

If p is true and q is false, what is the truth value of p ∧ q?

a)

True

b)

False

c)

Undetermined

d)

None

44.

If p is false and q is true, what is the truth value of p ∨ q?

a)

True

b)

False

c)

Undetermined

d)

None

45.

Which of the following is logically equivalent to p → q?

a)

¬p ∨ q

b)

p ∧ q

c)

¬p ∧ q

d)

p ∨ q

46.

When is the statement “p ↔ q” true?

a)

p and q have the same truth value

b)

p and q have different truth values

c)

p is true and q is false

d)

p is false and q is true

47.

What is the truth value of “If 2 + 2 = 4, then 3 + 3 = 6”?

a)

True

b)

False

c)

Undetermined

d)

None

48.

What is the truth value of “If 2 + 2 = 5, then 3 + 3 = 7”?

a)

True

b)

False

c)

Undetermined

d)

None

49.

What is the converse of “If a number is even, then it is divisible by 2”?

a)

If a number is divisible by 2, then it is even.

b)

If a number is not even, then it is not divisible by 2.

c)

If a number is not divisible by 2, then it is not even.

d)

If a number is even, then it is not divisible by 2.

50.

What is the contrapositive of “If it is a triangle, then it has three sides”?

a)

If it does not have three sides, then it is not a triangle.

b)

If it has three sides, then it is a triangle.

c)

If it is not a triangle, then it does not have three sides.

d)

If it is a triangle, then it does not have three sides.

51.

If p is true and q is false, what is the truth value of p → q?

a)

True

b)

False

c)

Undetermined

d)

None

52.

If p represents “It is raining,” what is the symbolic form of “It is not raining”?

a)

¬p

b)

p ∧ q

c)

p ∨ q

d)

p → q

53.

If p is “The number is even” and q is “The number is divisible by 2,” what is the symbolic form of “The number is even and divisible by 2”?

a)

p ∧ q

b)

p ∨ q

c)

p → q

d)

¬p

54.

If p is “It is sunny” and q is “I go outside,” what is the symbolic form of “If it is sunny, then I go outside”?

a)

p → q

b)

p ∧ q

c)

p ∨ q

d)

¬p → q

55.

If p is “I study” and q is “I pass,” what is the symbolic form of “If I study, then I pass”?

a)

p → q

b)

q → p

c)

p ∧ q

d)

p ∨ q

56.

If p is “It is raining” and q is “It is cloudy,” what is the symbolic form of “It is raining or it is cloudy”?

a)

p ∨ q

b)

p ∧ q

c)

p → q

d)

¬p

57.

If p is “The program runs” and q is “The code is correct,” what is the symbolic form of “The program runs if and only if the code is correct”?

a)

p ↔ q

b)

p → q

c)

p ∧ q

d)

p ∨ q

58.

If p is “I go to school” and q is “It is a holiday,” what is the symbolic form of “I will not go to school if it is a holiday”?

a)

q → ¬p

b)

p → ¬q

c)

¬p → q

d)

p ∧ q

59.

If p is “The number is odd,” what is the symbolic form of “The number is not odd”?

a)

¬p

b)

p ∧ q

c)

p ∨ q

d)

p → q

60.

If p is “It is Monday” and q is “I have class,” what is the symbolic form of “It is Monday and I have class”?

a)

p ∧ q

b)

p ∨ q

c)

p → q

d)

¬p

61.

If p is “I study” and q is “I pass,” what is the symbolic form of “If I do not study, then I do not pass”?

a)

¬p → ¬q

b)

p → q

c)

¬q → ¬p

d)

p ∧ q

62.

If p is “The triangle is equilateral” and q is “The triangle is isosceles,” what is the symbolic form of “The triangle is equilateral or isosceles”?

a)

p ∨ q

b)

p ∧ q

c)

p → q

d)

¬p

63.

If p is “The input is valid” and q is “The program executes,” what is the symbolic form of “If the input is valid, then the program executes”?

a)

p → q

b)

q → p

c)

p ∧ q

d)

p ∨ q

64.

If p is “It is sunny” and q is “It is cold,” what is the symbolic form of “It is not sunny and it is cold”?

a)

¬p ∧ q

b)

p ∧ q

c)

¬p ∨ q

d)

p → q

65.

If p is “I study” and q is “I pass,” what is the symbolic form of “I will pass if and only if I study”?

a)

p ↔ q

b)

p → q

c)

p ∧ q

d)

p ∨ q

66.

If p is “The number is positive” and q is “The number is even,” what is the symbolic form of “The number is positive or even”?

a)

p ∨ q

b)

p ∧ q

c)

p → q

d)

¬p

67.

If p is “The code is error-free” and q is “The program runs,” what is the symbolic form of “If the code is error-free, then the program runs”?

a)

p → q

b)

q → p

c)

p ∧ q

d)

p ∨ q

68.

If p is “It is raining” and q is “It is sunny,” what is the symbolic form of “It is not raining or it is sunny”?

a)

¬p ∨ q

b)

p ∧ q

c)

p → q

d)

¬p ∧ q

69.

If p is “I attend class” and q is “I learn,” what is the symbolic form of “If I attend class, then I learn”?

a)

p → q

b)

q → p

c)

p ∧ q

d)

p ∨ q

70.

If p is “The number is divisible by 2,” what is the symbolic form of “The number is not divisible by 2”?

a)

¬p

b)

p ∧ q

c)

p ∨ q

d)

p → q

71.

If p is “The input is correct” and q is “The program crashes,” what is the symbolic form of “The program does not crash if the input is correct”?

a)

p → ¬q

b)

¬p → q

c)

p ∧ q

d)

p ∨ q

72.

If p is “It is a weekend” and q is “I rest,” what is the symbolic form of “It is a weekend and I rest”?

a)

p ∧ q

b)

p ∨ q

c)

p → q

d)

¬p

73.

If p is “It is a weekend” and q is “I rest,” what is the symbolic form of “If I do not rest, then it is not a weekend”?

a)

¬q → ¬p

b)

p → q

c)

q → p

d)

p ∧ q

74.

If p is “The shape is a square” and q is “The shape has four equal sides,” what is the symbolic form of “The shape is a square if and only if it has four equal sides”?

a)

p ↔ q

b)

p → q

c)

p ∧ q

d)

p ∨ q

75.

If p is “The number is odd” and q is “The number is prime,” what is the symbolic form of “The number is odd or prime”?

a)

p ∨ q

b)

p ∧ q

c)

p → q

d)

¬p

76.

If p is “It is raining” and q is “The ground is wet,” what is the symbolic form of “It is raining if and only if the ground is wet”?

a)

p ↔ q

b)

p → q

c)

p ∧ q

d)

p ∨ q