{"id":3105,"date":"2025-06-09T10:12:20","date_gmt":"2025-06-09T10:12:20","guid":{"rendered":"https:\/\/diznr.com\/?p=3105"},"modified":"2025-06-09T10:12:20","modified_gmt":"2025-06-09T10:12:20","slug":"day-04-part-01-discrete-mathematics-for-gate-in-hindi-proposition-and-its-application","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-04-part-01-discrete-mathematics-for-gate-in-hindi-proposition-and-its-application\/","title":{"rendered":"Day 04 Part 01- Discrete Mathematics for gate in Hindi-Proposition and it’s application"},"content":{"rendered":"

Day 04 Part 01- Discrete Mathematics for gate in Hindi-Proposition and it’s application<\/p>\n

[fvplayer id=”255″]<\/p>\n

Proposition and Its Applications<\/strong> (Discrete Mathematics for GATE – Day 04, Part 01)<\/h3>\n

1. What is a Proposition?<\/strong><\/h4>\n

A proposition<\/strong> is a declarative statement that is either true (T)<\/strong> or false (F)<\/strong> but not both simultaneously.<\/p>\n

Examples:<\/strong>
\u00a0“The sun rises in the east.” (True<\/strong>)
\u00a0“2 + 2 = 5.” (False<\/strong>)<\/p>\n

Non-examples (not propositions):
\u00a0“What is your name?” (Not declarative)
\u00a0“x + 5 = 10” (Truth value depends on x)<\/p>\n

2. Logical Connectives<\/strong><\/h4>\n

Propositions can be combined using logical operators<\/strong>:<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Operator<\/th>\nSymbol<\/th>\nExample<\/th>\nMeaning<\/th>\n<\/tr>\n<\/thead>\n
Negation<\/td>\n\u00acP\\neg P<\/span>\u00ac<\/span>P<\/span><\/span><\/span><\/span><\/td>\n“It is not raining”<\/td>\nOpposite truth value<\/td>\n<\/tr>\n
Conjunction<\/td>\nP\u2227QP \\land Q<\/span>P<\/span>\u2227<\/span><\/span>Q<\/span><\/span><\/span><\/span><\/td>\n“It is cold and raining”<\/td>\nTrue if both are true<\/td>\n<\/tr>\n
Disjunction<\/td>\nP\u2228QP \\lor Q<\/span>P<\/span>\u2228<\/span><\/span>Q<\/span><\/span><\/span><\/span><\/td>\n“It is cold or raining”<\/td>\nTrue if at least one is true<\/td>\n<\/tr>\n
Implication<\/td>\nP\u21d2QP \\Rightarrow Q<\/span>P<\/span>\u21d2<\/span><\/span>Q<\/span><\/span><\/span><\/span><\/td>\n“If it rains, then the road is wet”<\/td>\nFalse only if P is true and Q is false<\/td>\n<\/tr>\n
Biconditional<\/td>\nP\u21d4QP \\Leftrightarrow Q<\/span>P<\/span>\u21d4<\/span><\/span>Q<\/span><\/span><\/span><\/span><\/td>\n“You pass if and only if you study”<\/td>\nTrue when both have the same truth value<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

3. Truth Table for Implication (\u2192)<\/strong><\/h4>\n
\n\n\n\n\n\n\n\n\n
PP<\/span>P<\/span><\/span><\/span><\/span><\/th>\nQQ<\/span>Q<\/span><\/span><\/span><\/span><\/th>\nP\u21d2QP \\Rightarrow Q<\/span>P<\/span>\u21d2<\/span><\/span>Q<\/span><\/span><\/span><\/span><\/th>\n<\/tr>\n<\/thead>\n
T<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nF<\/td>\nT<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

4. Applications of Propositions<\/strong><\/h4>\n