Verified Solution • 2025–26 Session moderate

QJEEM19Maee63: JEE Main 2019 Mathematics - Class 11 JEEM19Maee63 Solution: For any two statements p and q, the negation of the expression…

For any two statements p and q, the negation of the expression
p ∨\vee (~p ∧\wedge q) is :

Multiple Choice Options

  • A p ↔\leftrightarrow q
  • B ~p ∧\wedge ~q
  • C p ∧\wedge q
  • D ~p ∨\vee ~q

Step-by-Step Verified Solution

∼\sim [p ∨\vee (~p ∧\wedge q)]

= ∼\sim p ∧\wedge ( ∼\sim ( ∼\sim p ∨\vee ∼\sim q)

= ∼\sim p ∧\wedge ( p ∨\vee ∼\sim q)

= ( ∼\sim p ∧\wedge p ) ∨\vee ( ∼\sim p ∧\wedge ∼\sim q)

= ( ∼\sim p ∧\wedge ∼\sim q) [ as ∼\sim p ∧\wedge p is always false)

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