Using Truth Tables

Question 1

In a truth table, how many rows are there for two variables?

Answer 1

There are 4 rows for two variables.

Question 2

True or False: The statement ‘A and B’ is true when both A and B are true.

Answer 2

True. The conjunction is only true when both operands are true.

Question 3

What is the result of ‘A or B’ when both A and B are false?

Answer 3

The result is false.

Question 4

True or False: The statement ‘A implies B’ is false when A is true and B is false.

Answer 4

True. The implication is only false in this scenario.

Question 5

In a truth table, how is the logical negation of a statement represented?

Answer 5

It is represented by flipping the truth value: true becomes false and vice versa.

Question 6

True or False: The disjunction ‘A or B’ is false if at least one of A or B is true.

Answer 6

False. The disjunction is true if at least one operand is true.

Question 7

What is the output of ‘A and not B’ when A is true and B is false?

Answer 7

The output is true.

Question 8

True or False: The expression ‘not (A and B)’ is equivalent to ‘not A or not B’.

Answer 8

True. This is known as De Morgan’s Law.

Question 9

How many possible truth values are there for three variables?

Answer 9

There are 8 possible truth values for three variables.

Question 10

True or False: In a truth table, each variable can only have a value of true or false.

Answer 10

True. Each variable is binary.

Question 11

What is the truth value of ‘A or B’ if both A and B are true?

Answer 11

The truth value is true.

Question 12

True or False: The expression ‘A implies B’ is true if both A and B are false.

Answer 12

True. An implication is true when the antecedent is false.

Question 13

What is the result of ‘not A’ when A is true?

Answer 13

The result is false.

Question 14

True or False: The expression ‘A and B’ is true if A is true and B is false.

Answer 14

False. The conjunction requires both to be true.

Question 15

In a truth table, what does a row represent?

Answer 15

A row represents a unique combination of truth values for the variables.

Question 16

True or False: The expression ‘A or B’ is true if A is false and B is true.

Answer 16

True. The disjunction is true if at least one operand is true.

Question 17

What is the result of ‘A and B’ when A is false and B is true?

Answer 17

The result is false.

Question 18

True or False: The expression ‘not (A or B)’ is equivalent to ‘not A and not B’.

Answer 18

True. This is another application of De Morgan’s Law.

Question 19

How is the logical conjunction represented in a truth table?

Answer 19

It is represented with an AND operator (∧).

Question 20

True or False: The statement ‘A implies B’ can be rewritten as ‘not A or B’.

Answer 20

True. This is the logical equivalence of implication.

Question 21

What is the output of ‘not (A and B)’ when both A and B are true?

Answer 21

The output is false.

Question 22

True or False: The truth table for ‘A or B’ has the same output as ‘not (not A and not B)’.

Answer 22

True. This is another application of De Morgan’s Law.

Question 23

What is the result of ‘A implies B’ when A is false?

Answer 23

The result is true.

Question 24

True or False: A truth table can be used to determine the validity of a logical argument.

Answer 24

True. It can show if the conclusion follows from the premises.

Question 25

What does a truth table for a compound statement show?

Answer 25

It shows the truth values for all possible combinations of the component statements.

Question 26

True or False: The expression 'A and A' is equivalent to A.

Answer 26

True. This is known as idempotent law.

Question 27

What is the result of 'A or A'?

Answer 27

The result is A.

Question 28

True or False: The statement 'not (A or B)' is true when both A and B are false.

Answer 28

True. The negation of a disjunction is true only when both are false.

Question 29

What is the output of 'A and (B or C)' when A is true, B is false, and C is true?

Answer 29

The output is true.

Question 30

True or False: The expression 'A or (B and C)' is true if either A is true or both B and C are true.

Answer 30

True. This follows the rules of disjunction and conjunction.

Question 31

What is the result of 'not (A implies B)' when A is true and B is false?

Answer 31

The result is true.

Question 32

True or False: The expression 'A and B and C' is true if any one of A, B, or C is true.

Answer 32

False. All must be true for the conjunction to be true.

Question 33

What does the truth table for 'A and B' look like?

Answer 33

It shows true only when both A and B are true.

Question 34

True or False: The logical equivalence of 'A or not A' is always true.

Answer 34

True. This is known as the law of excluded middle.

Question 35

What is the output of 'not (not A)'?

Answer 35

The output is A.

Question 36

True or False: The expression 'not (A and B)' is true if either A or B is false.

Answer 36

True. The negation of a conjunction is true when at least one is false.

Question 37

What is the result of 'A or B' when A is true and B is true?

Answer 37

The result is true.

Question 38

True or False: The statement 'A implies B' is equivalent to 'B if A'.

Answer 38

True. This is a valid interpretation of implication.

Question 39

What is the output of 'A and (not B)' when A is false?

Answer 39

The output is false.

Question 40

True or False: The expression 'A or (B and C)' is false if A is false, B is false, and C is false.

Answer 40

True. The disjunction is false only when all operands are false.

Question 41

What does the truth table for 'not A' look like?

Answer 41

It shows true when A is false and false when A is true.

Question 42

True or False: The expression 'A and B' can be true if A is false and B is true.

Answer 42

False. Both A and B must be true for the conjunction to be true.

Question 43

What is the result of 'A or not A'?

Answer 43

The result is always true.

Question 44

What is the output of 'A implies B' when both A and B are true?

Answer 44

The output is true.

Question 45

True or False: The logical statement 'A and B' can be represented as 'B and A'.

Answer 45

True. This is known as the commutative property.