New Operator Concept-GATE 2025-Using-Discrete mathematics previous year paper-A binary logic relation

Ali Seron Jason

5 months ago

New Operator Concept-GATE 2021-Using-Discrete mathematics previous year paper-A binary logic relation

https://www.gyanodhan.com/video/7B4.%20GATE%20CSEIT/Discrete%20Mathematics%201/456.%20New%20Operator%20Concept-GATE%202006-Using-Discrete%20mathematics%20previous%20year%20paper-A%20binary%20logic%20relatio.mp4

Great! Let’s dive into the “New Operator Concept” from GATE 2025 preparation, particularly in Discrete Mathematics — focused on Binary Logical Relations and Previous Year Paper questions.

This is especially important because GATE sometimes introduces custom or new operators in logic questions (like #, @, *, etc.) and asks you to evaluate expressions based on given truth conditions.

Contents

1 New Operator Concept in Binary Logic – GATE Style

New Operator Concept in Binary Logic – GATE Style

Discrete Mathematics – Binary Logical Relation

1. What is a “New Operator”?

GATE often defines a new binary operator with a custom truth table. You must understand and apply that operator just like AND (∧), OR (∨), etc.

2. Example Question:

Operator Definition:
Let P # Q be a binary logical operator defined as:
P # Q = True only when exactly one of P or Q is True.
In all other cases, P # Q = False.

This is exclusive OR (XOR) in disguise.

Truth Table for P # Q:

P	Q	P # Q
T	T	F
T	F	T
F	T	T
F	F	F

3. GATE PYQ Style Question:

Q: Suppose the operator * is defined such that:
P * Q = ¬(P ∧ Q) ∨ (P Q).
What is the truth value of (T * F)?

Solution Steps:

P = T, Q = F
P ∧ Q = F → ¬(F) = T
P Q = F
Final: T ∨ F = T

Answer: True

4. Key Concepts for Solving These:

Follow truth tables precisely.
Understand logical equivalence:
- ¬(P ∧ Q) = ¬P ∨ ¬Q (DeMorgan)
- P Q = (P → Q) ∧ (Q → P)
Break down complex expressions step by step.

5. Strategy to Tackle These in GATE:

Step	What to Do
Read Definition	Carefully read how the operator behaves
Build Truth Table	If time permits, build all 4 cases
Break Down	Solve inner expressions first (brackets)
Time Management	Practice similar PYQs to get faster

Tip: Practice These Operator Forms:

P # Q = (¬P ∧ Q) ∨ (P ∧ ¬Q) → XOR
P @ Q = P ∨ (¬P ∧ Q) → Custom
P * Q = ¬(P Q) → Logical difference

Would you like:

A PDF worksheet with past GATE questions on new operators?
A truth table quiz to practice?
Hindi video or notes on this concept?

Let me know what works best for your GATE 2025 preparation!

New Operator Concept-GATE 2025-Using-Discrete mathematics previous year paper-A binary logic relation

New Operator Concept in Binary Logic – GATE Style