Question

Download Solution PDF

“If X, then Y unless Z” is represented by which of the following formulae in propositional logic ?

This question was previously asked in
UGC NET Computer Science (Paper 3) Nov 2017 Official Paper
Attempt in App
View all UGC NET Papers >

Answer (Detailed Solution Below)

Option 2 :
Free Tests
View all Free tests >
Free
UGC NET Paper 1: Held on 21st August 2024 Shift 1
50 Qs. 100 Marks 60 Mins
Start Now

Detailed Solution

Download Solution PDF

The correct answer is option 2.

Key Points

“If X, then Y unless Z”  means   

Hence Option 2 only matches 
Hence the correct answer is

Download Solution PDF
Latest UGC NET Updates

Last updated on Jun 25, 2025

-> The UGC Net Admit Card has been released on its official website today.

-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.

-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.

-> The exam is conducted bi-annually - in June and December cycles.

-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions. 

-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.

Exams Tests Super Practice

More Propositional Logic Questions

Q1.Match the LIST-I with LIST-II: Match the logical equivalence propositions LIST - I LIST - II A. P → q I. (p ∧ q) ∨(¬p ∨ ¬q) B. ¬(p ∨ (¬p ∧ q)) II. ¬p ∨ q C. p ↔ q III. ¬(p ∨ q) D. ¬(p ↔ q) IV. ¬p ↔ q Choose the correct answer from the options given below:
Q2.The mathematical notation to describe logical entailment of a scentence "α entails another sentence β" is
Q3.Given below are two statements: Statement (I): If H is non empty finite subset of a group G and ab ∈ H ∀ a, b ∈ H, then H is also a group Statement (II): There is no homomorphism exist from (Z, +) to (Q. +); where Z is set of integers and Q is set of rational number. In the light of the above statements, choose the most appropriate answer from the options given below:
Q4.Given below are two statements: Statement I: "Grandparent is a parent of one's parent". Statement II: First Order Predicate Logic (FOPL) representation of above statement is ∀ g, c grandparent (g, c) ⇔ ∃ p parent (g, p) ∧ parent (p, c) In the light of the above statements, choose the most appropriate answer from the options given below:
Q5.Consider the sentence below. There is a country that borders both India and Pakistan. Which of the following logical expressions express the above sentence correctly when the predicate Country(x) represents that x is a country and Borders(x, y) represents that the countries x and y share the border?
Q6.What is logically equivalent to the following statements? "I pass only if you pass" (Note that fail is equivalent to not pass.)
Q7.Consider the following logical inferences. I1: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I2: If it rains then the cricket match will not be played. It did not rain Inference: The cricket match was played. Which of the following is TRUE?
Q8.Which one of the following is NOT logically equivalent to ¬ ∃x (∀ y (α) ∧ ∀ z(β))?
Q9.Which of the following pairs of propositions are not logically equivalent ?
Q10.Which of the following statements are true ? (A) A sentence α entails another sentence β  if β is true in few worlds where α is true. (B) Forward chaining and backward chaining are very natural reasoning algorithms for knowledge bases in Horn form. (C) Sound inference algorithms derive all sentences that are entailed. (D) Propositional logic does not scale to environments of unbounded size. Choose the correct answer from the options given below:

More Mathematical Logic Questions

Q1.Let the predicates D(x, y) mean “team x defeated team y” and P(x, y) mean “team x has played team y”. The quantified formula for the statement that there is a team that has beaten every team it has played, is :
Q2.Match the LIST-I with LIST-II: Match the logical equivalence propositions LIST - I LIST - II A. P → q I. (p ∧ q) ∨(¬p ∨ ¬q) B. ¬(p ∨ (¬p ∧ q)) II. ¬p ∨ q C. p ↔ q III. ¬(p ∨ q) D. ¬(p ↔ q) IV. ¬p ↔ q Choose the correct answer from the options given below:
Q3.The mathematical notation to describe logical entailment of a scentence "α entails another sentence β" is
Q4.The statement among the following that is a tautology is:
Q5.The logical statement (p ⇒ q) ∧ (q ⇒∼ p) is equivalent to
Q6.For the statements p and q, consider the following compound statements: (a) (~q∧(p → q)) → ~p (b) ((p∨q))∧~p) → q Then which of the following statements is correct?
Q7.The negation of the statement ~p∧(p∨q) is∶
Q8.Which of the following statements is a tautology?
Q9.If the universe of disclosure is set of integers, then which of the followings are TRUE? (A) ∀n ∃m(n2 < m) (B) ∃n ∀m(n < m2) (C) ∃n ∀m(nm = m) (D) ∃n ∃m(n2 + m2 = 6) (E) ∃n ∃m(n + m = 4 ∧ n - m = 1) Choose the correct answer from the options given below:
Q10.Arrange the following in ascending order: (A) Remainder of 4916 when divided by 17 (B) Remainder of 2446 when divided by 9 (C) Remainder of 15517 when divided by 17 (D) Last digits of the number 745 Choose the correct answer from the options given below:

UGC NET Important Links

Exam AnalysisAdmit CardExam DatesApplication FormEligibilityUGC NET Syllabus

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti club apk all teen patti game teen patti rummy teen patti gold new version 2024