Question
Download Solution PDFLet P and Q be two propositions, ¬ (P ↔ Q) is equivalent to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula:
¬ (P ↔ Q) = (¬P ↔ Q) = (P ↔ ¬Q)
Truth Table:
|
P |
¬ P |
Q |
¬ Q |
¬ (P ↔ Q) |
¬ P ↔ Q |
P ↔ ¬ Q |
¬ P ↔ ¬ Q |
Q → P |
|
F |
T |
F |
T |
F |
F |
F |
T |
T |
|
F |
T |
T |
F |
T |
T |
T |
F |
F |
|
T |
F |
F |
T |
T |
T |
T |
F |
T |
|
T |
F |
T |
F |
F |
F |
F |
T |
T |
Therefore, ¬ (P ↔ Q) is equivalent to (¬P ↔ Q) and (P ↔ ¬Q)
Hence option 1 is correct.
Important Points:
(P ↔ Q) ≡ p ⊙ q
¬ (P ↔ Q) ≡ p ⊕ q
Mistake Points
Option 2: ¬ P ↔ Q is changed to ¬ P → Q
Last updated on Jun 6, 2025
-> The UGC NET Exam Schedule 2025 for June has been released on its official website.
-> The UGC NET Application Correction Window 2025 is available from 14th May to 15th May 2025.
-> The UGC NET 2025 online application form submission closed on 12th May 2025.
-> The June 2025 Exam will be conducted from 21st June to 30th 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.