Consider following two rules R1 and R2 in logical reasoning in Artificial Intelligence (AI) : R1 : From α ⊃ β and α Infer β is known as Modus Tollens (MT) R2 : From α ⊃ β and ¬β Infer ¬α is known as Modus Ponens (MP)
Neither R1 nor R2 is correct.
Here α ⊃ β denotes the implication “if α then β”. Two classical rules of inference use an implication as one premise.
Modus Ponens (MP): from α ⊃ β and α, infer β (affirming the antecedent).
Modus Tollens (MT): from α ⊃ β and ¬β, infer ¬α (denying the consequent).
R1 states the pattern “from α ⊃ β and α infer β”, which is Modus Ponens, but names it Modus Tollens. R1 is therefore not correct.
R2 states the pattern “from α ⊃ β and ¬β infer ¬α”, which is Modus Tollens, but names it Modus Ponens. R2 is therefore not correct.
Both inference patterns are valid in themselves, but each rule is attached to the other's name, so claiming R1, R2 or both as correct is wrong.
Neither R1 nor R2 is correct. option is correct.
Similar Questions
The resolvent of the set of clauses
\((A \lor B,\ \sim A \lor D,\ C \lor \sim B)\) is
In Propositional Logic, given P and \(P \to Q\), we can infer __________.
A horn clause is __________.
Which of the following arguments are not valid ?
(a) “ If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard”.
(b) “Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty”.
(c) If n is a real number such that \(n \gt 1\), then \(n^{2} \gt 1\). Suppose that \(n^{2} \gt 1\), then \(n \gt 1\).
Codes :
The clausal form of the disjunctive normal form \(\neg A \vee \neg B \vee \neg C \vee D\) is :
“If my computations are correct and I pay the electric bill, then I will run out of money. If I don’t pay the electric bill, the power will be turned off. Therefore, if I don’t run out of money and the power is still on, then my computations are incorrect.”
Convert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where ¬ means NOT)
Give a compound proposition involving propositions p, q and r that is true when exactly two of p, q and r are true and is false otherwise.
How many different truth tables of the compound propositions are there that involve the propositions p & q ?
Let P be “It is hot day” and q be “The temperature is 48°C”. Write in simple sentences the meaning of ~p∧~q.
Consider the statement,
“Either – 2 ≤ x ≤ – 1 or 1 ≤ x ≤2”.
The negation of this statement is
Important Questions from Propositional Logic
- Assume that a Creative ($C$) person will Succeed ($S$) if the person is also Disciplined ($D$), but will not succeed otherwise. Now, consider the following statements:
(i) $C \land S \Leftrightarrow D$
(ii) $C \Rightarrow (S \Leftrightarrow D)$
(iii) $C \Leftrightarrow ((D \Rightarrow S) \lor \neg S)$
Which of the following options is correct? - Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies?
Let $p$ and $q$ be any two propositions. Consider the following propositional statements.
$S_1: p \to q$ $S_2: \neg p \land q$ $S_3: \neg p \lor q$ $S_4 : \neg p \lor \neg q$
where $\land$ denotes conjunction (AND operation), $\lor$ denotes disjunction (OR operation), and $\neg$ denotes negation (NOT operation). Which one of the following options is correct?
(Note: $\equiv$ denotes logical equivalence)Which of the following logical implications are tautology?
A. $[\sim p \land (p \lor q)] \rightarrow q$
B. $\sim p \rightarrow (p \rightarrow q)$
C. $[p \land (p \rightarrow q)] \rightarrow q$
D. $\sim (p \rightarrow q) \rightarrow q$
Choose the correct answer from the options given below:
- Sentence $X$ is said to entail Sentence $Y$ if whenever $X$ is $TRUE$, $Y$ also must hold $TRUE$.
Which of the following statements is/are correct if $X$ entails $Y$?
