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Question

Mathematics Question on types of differential equations

The negation of the expression q∨((∼q)∧p)q \vee((\sim q) \wedge p) is equivalent to

A

p∧(∼q)p \wedge(\sim q)

B

(∼p)∧(∼q)(\sim p) \wedge(\sim q)

C

(∼p)∨(∼q)(\sim p) \vee(\sim q)

D

(∼p)∨q(\sim p) \vee q

Answer

(∼p)∧(∼q)(\sim p) \wedge(\sim q)

Explanation

Solution

∼(q∨((∼q)∧p))
=∼q∧∼((∼q)∧p)
=∼q∧(q∨∼p)
=(∼q∧q)∨(∼q∧∼p)
=(∼q∧∼p)