{"id":2946,"date":"2025-06-07T07:11:07","date_gmt":"2025-06-07T07:11:07","guid":{"rendered":"https:\/\/diznr.com\/?p=2946"},"modified":"2025-06-07T07:11:07","modified_gmt":"2025-06-07T07:11:07","slug":"new-operator-concept-gate-2021-using-discrete-mathematics-previous-year-paper-a-binary-relation-logic","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/new-operator-concept-gate-2021-using-discrete-mathematics-previous-year-paper-a-binary-relation-logic\/","title":{"rendered":"New Operator Concept-GATE 2025-Using-Discrete mathematics previous year paper-A binary logic relation"},"content":{"rendered":"

New Operator Concept-GATE 2021-Using-Discrete mathematics previous year paper-A binary logic relation<\/p>\n

[fvplayer id=”183″]<\/p>\n

Great! Let\u2019s dive into the \u201cNew Operator Concept\u201d<\/strong> from GATE 2025<\/strong> preparation, particularly in Discrete Mathematics<\/strong> \u2014 focused on Binary Logical Relations<\/strong> and Previous Year Paper<\/strong> questions.<\/p>\n

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

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\ud83e\udde0 New Operator Concept in Binary Logic \u2013 GATE Style<\/strong><\/h2>\n

\ud83d\udcd8 Discrete Mathematics \u2013 Binary Logical Relation<\/strong><\/h3>\n

\ud83d\udccc 1. What is a “New Operator”?<\/strong><\/h3>\n

GATE often defines a new binary operator<\/strong> with a custom truth table<\/strong>. You must understand and apply that operator just like AND (\u2227), OR (\u2228), etc.<\/p>\n

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\ud83e\uddea 2. Example Question:<\/strong><\/h3>\n
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Operator Definition:<\/strong>
Let P # Q<\/strong> be a binary logical operator defined as:
P # Q = True<\/strong> only when exactly one<\/strong> of P or Q is True<\/strong>.
In all other cases, P # Q = False.<\/p>\n<\/blockquote>\n

This is exclusive OR (XOR)<\/strong> in disguise.<\/p>\n

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\u2705 Truth Table for P # Q:<\/strong><\/h3>\n
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\n\n\n\n\n\n\n\n\n
P<\/th>\nQ<\/th>\nP # Q<\/th>\n<\/tr>\n<\/thead>\n
T<\/td>\nT<\/td>\nF<\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\ud83d\udcdd 3. GATE PYQ Style Question:<\/strong><\/h3>\n
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Q:<\/strong> Suppose the operator *<\/code> is defined such that:
P * Q = \u00ac(P \u2227 Q) \u2228 (P \u2194 Q).
What is the truth value of (T * F)?<\/p>\n<\/blockquote>\n

\ud83d\udcd8 Solution Steps:<\/strong><\/p>\n

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  1. \n

    P = T, Q = F<\/p>\n<\/li>\n

  2. \n

    P \u2227 Q = F \u2192 \u00ac(F) = T<\/p>\n<\/li>\n

  3. \n

    P \u2194 Q = F<\/p>\n<\/li>\n

  4. \n

    Final: T \u2228 F = T<\/strong><\/p>\n<\/li>\n<\/ol>\n

    \u2705 Answer: True<\/strong><\/p>\n

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    \u2699\ufe0f 4. Key Concepts for Solving These:<\/strong><\/h3>\n