Logic Made Easy : Solution Manual for A
Concise Introduction to Logic 12th Edition
What is a causal fallacy?
A causal fallacy is an error in reasoning that establishes a cause-and-effect relationship without
sufficient evidence.
What is a syllogistic fallacy?
A syllogistic fallacy occurs when the premises of a syllogism do not logically lead to the
conclusion.
What is a valid argument?
A valid argument is one where if the premises are true, the conclusion must also be true,
regardless of the actual truth of the premises.
What is a sound argument?
A sound argument is a valid argument with all true premises, guaranteeing the truth of the
conclusion.
What is a logical equivalence?
Logical equivalence occurs when two statements are true in the same situations, meaning they
have the same truth value.
What is a conditional statement?
A conditional statement is a logical statement that expresses a relationship between two
propositions, typically in the form 'If P, then Q.'
What is a biconditional statement?
A biconditional statement is a logical statement that is true if both components are either true or
false, expressed as 'P if and only if Q.'
What is a quantifier?
A quantifier is a term used in logic to indicate the scope of a statement, such as 'all,' 'some,' or
'none.'
What is disjunction in propositional logic?
The disjunction of propositions p and q is denoted by p ∨ q, which is true if at least one of p or q
is true.
What is the difference between inclusive or and exclusive or?
Inclusive or (p ∨ q) allows both to be true; exclusive or (p ⊕ q) allows only one to be true.
What does implication p → q represent?
It is read as 'if p, then q' and is true unless p is true and q is false.
What is the truth table for implication?
T T = T; T F = F; F T = T; F F = T.
What is the contrapositive of p → q?
¬q → ¬p.
What is the converse of p → q?
q → p.
What is the inverse of p → q?
¬p → ¬q.
What is a biconditional proposition?
Denoted by p ↔ q, it is true if both p and q are either true or false.
, What is the precedence of the logical operator ¬?
1 (highest precedence)
What is the precedence of the logical operator ∧?
2
What is the precedence of the logical operator ∨?
3
What is the precedence of the logical operator →?
4
What is the precedence of the logical operator ↔?
5 (lowest precedence)
How do you translate the sentence 'If I go to Harry's or to the country, I will not go
shopping' into propositional logic?
p ∨ q → ¬r, where p: I go to Harry's, q: I go to the country, r: I will go shopping.
How would you express 'The automated reply cannot be sent when the file system is full' in
propositional logic?
q → ¬p, where p: The automated reply can be sent, q: The file system is full.
What is Disjunctive Normal Form (DNF)?
A propositional formula that consists of a disjunction of disjuncts, where each disjunct consists
of a conjunction of atomic formulas or their negations.
What is Conjunctive Normal Form (CNF)?
A compound proposition that is a conjunction of disjunctions.
What is propositional satisfiability?
A compound proposition is satisfiable if there is an assignment of truth values that makes it true.
What is the solution for the satisfiability of the proposition 'p ∧ q'?
Satisfiable; assign T to both p and q.
What is the solution for the satisfiability of the proposition 'p ∧ ¬p'?
Not satisfiable; no assignment can make it true.
What are the Identity Laws in logic?
p ∨ T = T and p ∧ F = F.
What are the Domination Laws in logic?
p ∨ F = p and p ∧ T = p.
What are the Idempotent Laws in logic?
p ∨ p = p and p ∧ p = p.
What is the Double Negation Law?
¬(¬p) = p.
What are the Commutative Laws in logic?
p ∨ q = q ∨ p and p ∧ q = q ∧ p.
What are the Associative Laws in logic?
(p ∨ q) ∨ r = p ∨ (q ∨ r) and (p ∧ q) ∧ r = p ∧ (q ∧ r).
What are the Absorption Laws in logic?
p ∨ (p ∧ q) = p and p ∧ (p ∨ q) = p.
What is the definition of logic?
the study of the principle of correct reasoning
What does logic have to do with God?
It is the way God thinks
Is atheism a religious belief? Why or why not?
Concise Introduction to Logic 12th Edition
What is a causal fallacy?
A causal fallacy is an error in reasoning that establishes a cause-and-effect relationship without
sufficient evidence.
What is a syllogistic fallacy?
A syllogistic fallacy occurs when the premises of a syllogism do not logically lead to the
conclusion.
What is a valid argument?
A valid argument is one where if the premises are true, the conclusion must also be true,
regardless of the actual truth of the premises.
What is a sound argument?
A sound argument is a valid argument with all true premises, guaranteeing the truth of the
conclusion.
What is a logical equivalence?
Logical equivalence occurs when two statements are true in the same situations, meaning they
have the same truth value.
What is a conditional statement?
A conditional statement is a logical statement that expresses a relationship between two
propositions, typically in the form 'If P, then Q.'
What is a biconditional statement?
A biconditional statement is a logical statement that is true if both components are either true or
false, expressed as 'P if and only if Q.'
What is a quantifier?
A quantifier is a term used in logic to indicate the scope of a statement, such as 'all,' 'some,' or
'none.'
What is disjunction in propositional logic?
The disjunction of propositions p and q is denoted by p ∨ q, which is true if at least one of p or q
is true.
What is the difference between inclusive or and exclusive or?
Inclusive or (p ∨ q) allows both to be true; exclusive or (p ⊕ q) allows only one to be true.
What does implication p → q represent?
It is read as 'if p, then q' and is true unless p is true and q is false.
What is the truth table for implication?
T T = T; T F = F; F T = T; F F = T.
What is the contrapositive of p → q?
¬q → ¬p.
What is the converse of p → q?
q → p.
What is the inverse of p → q?
¬p → ¬q.
What is a biconditional proposition?
Denoted by p ↔ q, it is true if both p and q are either true or false.
, What is the precedence of the logical operator ¬?
1 (highest precedence)
What is the precedence of the logical operator ∧?
2
What is the precedence of the logical operator ∨?
3
What is the precedence of the logical operator →?
4
What is the precedence of the logical operator ↔?
5 (lowest precedence)
How do you translate the sentence 'If I go to Harry's or to the country, I will not go
shopping' into propositional logic?
p ∨ q → ¬r, where p: I go to Harry's, q: I go to the country, r: I will go shopping.
How would you express 'The automated reply cannot be sent when the file system is full' in
propositional logic?
q → ¬p, where p: The automated reply can be sent, q: The file system is full.
What is Disjunctive Normal Form (DNF)?
A propositional formula that consists of a disjunction of disjuncts, where each disjunct consists
of a conjunction of atomic formulas or their negations.
What is Conjunctive Normal Form (CNF)?
A compound proposition that is a conjunction of disjunctions.
What is propositional satisfiability?
A compound proposition is satisfiable if there is an assignment of truth values that makes it true.
What is the solution for the satisfiability of the proposition 'p ∧ q'?
Satisfiable; assign T to both p and q.
What is the solution for the satisfiability of the proposition 'p ∧ ¬p'?
Not satisfiable; no assignment can make it true.
What are the Identity Laws in logic?
p ∨ T = T and p ∧ F = F.
What are the Domination Laws in logic?
p ∨ F = p and p ∧ T = p.
What are the Idempotent Laws in logic?
p ∨ p = p and p ∧ p = p.
What is the Double Negation Law?
¬(¬p) = p.
What are the Commutative Laws in logic?
p ∨ q = q ∨ p and p ∧ q = q ∧ p.
What are the Associative Laws in logic?
(p ∨ q) ∨ r = p ∨ (q ∨ r) and (p ∧ q) ∧ r = p ∧ (q ∧ r).
What are the Absorption Laws in logic?
p ∨ (p ∧ q) = p and p ∧ (p ∨ q) = p.
What is the definition of logic?
the study of the principle of correct reasoning
What does logic have to do with God?
It is the way God thinks
Is atheism a religious belief? Why or why not?
