Using Truth Tables Flashcards
In a truth table, how many rows are there for two variables?
There are 4 rows for two variables.
True or False: The statement ‘A and B’ is true when both A and B are true.
True. The conjunction is only true when both operands are true.
What is the result of ‘A or B’ when both A and B are false?
The result is false.
True or False: The statement ‘A implies B’ is false when A is true and B is false.
True. The implication is only false in this scenario.
In a truth table, how is the logical negation of a statement represented?
It is represented by flipping the truth value: true becomes false and vice versa.
True or False: The disjunction ‘A or B’ is false if at least one of A or B is true.
False. The disjunction is true if at least one operand is true.
What is the output of ‘A and not B’ when A is true and B is false?
The output is true.
True or False: The expression ‘not (A and B)’ is equivalent to ‘not A or not B’.
True. This is known as De Morgan’s Law.
How many possible truth values are there for three variables?
There are 8 possible truth values for three variables.
True or False: In a truth table, each variable can only have a value of true or false.
True. Each variable is binary.
What is the truth value of ‘A or B’ if both A and B are true?
The truth value is true.
True or False: The expression ‘A implies B’ is true if both A and B are false.
True. An implication is true when the antecedent is false.
What is the result of ‘not A’ when A is true?
The result is false.
True or False: The expression ‘A and B’ is true if A is true and B is false.
False. The conjunction requires both to be true.
In a truth table, what does a row represent?
A row represents a unique combination of truth values for the variables.
True or False: The expression ‘A or B’ is true if A is false and B is true.
True. The disjunction is true if at least one operand is true.
What is the result of ‘A and B’ when A is false and B is true?
The result is false.
True or False: The expression ‘not (A or B)’ is equivalent to ‘not A and not B’.
True. This is another application of De Morgan’s Law.
How is the logical conjunction represented in a truth table?
It is represented with an AND operator (∧).
True or False: The statement ‘A implies B’ can be rewritten as ‘not A or B’.
True. This is the logical equivalence of implication.
What is the output of ‘not (A and B)’ when both A and B are true?
The output is false.
True or False: The truth table for ‘A or B’ has the same output as ‘not (not A and not B)’.
True. This is another application of De Morgan’s Law.
What is the result of ‘A implies B’ when A is false?
The result is true.
True or False: A truth table can be used to determine the validity of a logical argument.
True. It can show if the conclusion follows from the premises.
What does a truth table for a compound statement show?
It shows the truth values for all possible combinations of the component statements.
True or False: The expression ‘A and A’ is equivalent to A.
True. This is known as idempotent law.
What is the result of ‘A or A’?
The result is A.
True or False: The statement ‘not (A or B)’ is true when both A and B are false.
True. The negation of a disjunction is true only when both are false.
What is the output of ‘A and (B or C)’ when A is true, B is false, and C is true?
The output is true.
True or False: The expression ‘A or (B and C)’ is true if either A is true or both B and C are true.
True. This follows the rules of disjunction and conjunction.
What is the result of ‘not (A implies B)’ when A is true and B is false?
The result is true.
True or False: The expression ‘A and B and C’ is true if any one of A, B, or C is true.
False. All must be true for the conjunction to be true.
What does the truth table for ‘A and B’ look like?
It shows true only when both A and B are true.
True or False: The logical equivalence of ‘A or not A’ is always true.
True. This is known as the law of excluded middle.
What is the output of ‘not (not A)’?
The output is A.
True or False: The expression ‘not (A and B)’ is true if either A or B is false.
True. The negation of a conjunction is true when at least one is false.
What is the result of ‘A or B’ when A is true and B is true?
The result is true.
True or False: The statement ‘A implies B’ is equivalent to ‘B if A’.
True. This is a valid interpretation of implication.
What is the output of ‘A and (not B)’ when A is false?
The output is false.
True or False: The expression ‘A or (B and C)’ is false if A is false, B is false, and C is false.
True. The disjunction is false only when all operands are false.
What does the truth table for ‘not A’ look like?
It shows true when A is false and false when A is true.
True or False: The expression ‘A and B’ can be true if A is false and B is true.
False. Both A and B must be true for the conjunction to be true.
What is the result of ‘A or not A’?
The result is always true.
What is the output of ‘A implies B’ when both A and B are true?
The output is true.
True or False: The logical statement ‘A and B’ can be represented as ‘B and A’.
True. This is known as the commutative property.
