New Operator Concept-GATE 2025-Using-Discrete mathematics previous year paper-A binary logic relation
New Operator Concept-GATE 2021-Using-Discrete mathematics previous year paper-A binary logic relation
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 [hide]
- 1
New Operator Concept in Binary Logic – GATE Style- 1.1
Discrete Mathematics – Binary Logical Relation - 1.2
1. What is a “New Operator”? - 1.3
2. Example Question: - 1.4
Truth Table for P # Q: - 1.5
3. GATE PYQ Style Question: - 1.6
4. Key Concepts for Solving These: - 1.7
5. Strategy to Tackle These in GATE: - 1.8
Tip: Practice These Operator Forms: - 1.9 New Operator Concept-GATE 2025-Using-Discrete mathematics previous year paper-A binary logic relation
- 1.10 Discrete Mathematics for Computer Science
- 1.11 GRADUATE APTITUDE TEST IN ENGINEERING 2025
- 1.12 Discrete Mathematics and Its Applications, Eighth Edition
- 1.1
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
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P ∧ Q = F → ¬(F) = T
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P ↔ Q = F
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Final: T ∨ F = T
Answer: True
4. Key Concepts for Solving These:
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Follow truth tables precisely.
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Understand logical equivalence:
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¬(P ∧ Q) = ¬P ∨ ¬Q (DeMorgan)
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P ↔ Q = (P → Q) ∧ (Q → P)
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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:
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P # Q = (¬P ∧ Q) ∨ (P ∧ ¬Q)→ XOR -
P @ Q = P ∨ (¬P ∧ Q)→ Custom -
P * Q = ¬(P ↔ Q)→ Logical difference
Would you like:
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A PDF worksheet with past GATE questions on new operators?
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A truth table quiz to practice?
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Hindi video or notes on this concept?
Let me know what works best for your GATE 2025 preparation!