Which one of the following is true ?
The resolvent of two Horn clauses is a Horn clause
A Horn clause has at most one positive literal.
When two Horn clauses are resolved, one positive literal is cancelled against its negation, so the resolvent keeps at most one positive literal and remains a Horn clause.
Resolving a negated goal (no positive literal) with a fact or rule gives another goal clause with no positive literal, which may be empty (null) or not, so both remaining statements are wrong.
Therefore closure of Horn clauses under resolution is the true statement.
Hence, The resolvent of two Horn clauses is a Horn clause.
Similar Questions
Match the following terms :
List - I List - II (a) Vacuous proof (i) A proof that the implication \(p \rightarrow q\) is true based on the fact that p is false. (b) Trivial proof (ii) A proof that the implication \(p \rightarrow q\) is true based on the fact that q is true. (c) Direct proof (iii) A proof that the implication \(p \rightarrow q\) is true that proceeds by showing that q must be true when p is true. (d) Indirect proof (iv) A proof that the implication \(p \rightarrow q\) is true that proceeds by showing that p must be false when q is false. Codes :
Consider a proposition given as :
“ \(x \geq 6\), if \(x^{2} \geq 25\) and its proof as :
If \(x \geq 6\), then \(x^{2} = x \cdot x \geq 6 \cdot 6 = 36 \geq 25\)
Which of the following is correct w.r.to the given proposition and its proof ?
(a) The proof shows the converse of what is to be proved.
(b) The proof starts by assuming what is to be shown.
(c) The proof is correct and there is nothing wrong.
The mathematical notation to describe logical entailment of a scentence “α entails another sentence β” is
Match the following :
List – I List – II a. Absurd i. Clearly impossible being contrary to some evident truth. b. Ambiguous ii. Capable of more than one interpretation or meaning. c. Axiom iii. An assertion that is accepted and used without a proof. d. Conjecture iv. An opinion preferably based on some experience or wisdom. Codes :
Important Questions from Mathematical Logic
Which of the following equation represents a function?
The value of \({4^{2{{\log }}3}}\) is
If \(\sqrt {1 + \frac{x}{{225}}} = \frac{{17}}{{15}}\) , then the value of x is
If \(x = 7 - 4\sqrt 3 \) then the value of \(x + \frac{1}{x}\) is
- \(\sqrt[3]{{\sqrt {0.000729} }} =\)
