The inference rule deals exclusively with formulas in conjunctive normal forms is called as :
Resolution rule
A formula in conjunctive normal form (CNF) is a conjunction of clauses, where each clause is a disjunction of literals.
The resolution rule works only on such clauses: from the clauses (P ∨ x) and (¬P ∨ y) it derives the resolvent (x ∨ y). Repeated resolution on a set of CNF clauses either produces the empty clause, proving the set unsatisfiable, or stops without it.
Because every premise and every conclusion of resolution is a clause, the rule deals exclusively with formulas in conjunctive normal form, and it is the basis of refutation theorem proving in propositional and first-order logic.
A contingency is a formula that is neither a tautology nor a contradiction, and unsatisfiability and contradiction are properties of formulas, not inference rules that operate on clauses.
Hence, Resolution rule.
Let \(\varphi, \psi\) be the formula, \(\varphi \models \Psi\), if and only if \(\varphi \models \Psi\) is a :
Which of the following relations defined on X = {1, 2, 3} is an equivalent relation ?
A rod is divided into six segment is to be colored with one or more of 4 different colors. In how many ways can this be done ?
Consider the following linear programming problem : Maximize \(z = 5x_{1} + 2x_{2} + 3x_{3} - x_{4} + x_{5}\) Subject to : \(x_{1} + 2x_{2} + 2x_{3} + x_{4} = 8\), \(3x_{1} + 4x_{2} + x_{3} + x_{5} = 7\), \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \geq 0\) What will be the basic feasible solution after iteration 1 ?
The thickness of a graph G is defined as minimum number of (edge-disjoint) planar subgraphs into which G can be decomposed. The thickness of G is defined as \(\theta(G)\). What is the thickness of planar graph ?
A committee is to be selected from 5 candidates a, b, c, d and e. The selection must satisfy all the following conditions :
• Either a or b must be included, but not both
• Either c or e or both must be included
• If d is included then b must be included
• Either a or c are included or neither is included.
• If e is included, then c and d must be included. How should selection be made ?
Let us consider the letters from a through h, and all 5 letters are made using these letters. (words are just strings of letters). How many of these words contain no repeated letters ?
Let us consider the following primal problem : Maximize \(z = 2x_{1} + x_{2}\) Subject to \(x_{1} - x_{2} \leq 4\), \(x_{1} - x_{2} \leq 2\), \(x_{1}, x_{2} \geq 0\) What will be its dual problem ?
Identify an appropriate operation sequence with respect to execution of a machine level language instruction.
The “instruction decode” phase in CPU’s instruction cycle is responsible to _____ .
.................... is a client server application that identifies each host on the internet with a unique user-friendly name.
Every OS has a ................ or .......... which primarily resides in the main memory of the computer to perform some of the basic functions of the OS.
(i) Kernel
(ii) Interface
(iii) Nucleus
(iv) Compiler
Codes:
Which of the following are referred to as low level language?
(i) Machine language
(ii) Assembly language
(iii) High level language
(iv) Natural language
Codes:
Match the following:
| List I | List II |
| (a) New York Public Library | (i) Shelv AR |
| (b) Miami University Augmented Research Group | (ii) Smart library |
| (c) Oula University Library | (iii) Wolf Walk |
| (d) North Carolina State University | (iv) Find the future |
Codes:
Which part of the QR code represents the encoded data?