The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:
- p ⇒ q
- q ⇒ p
- ~ (p ⇒ q)
- ~ (q ⇒ p)
The Correct Option is A
Solution and Explanation
The correct option is(C): ~ (p ⇒ q).
Let S : ((~ q) ∧ p) ⇒ ((~ p) ∨ q)
⇒ S : ~ ((~ q) ∧ p) ∨ ((~ p) ∨ q)
⇒ S : (q ∨ (~ p)) ∨ ((~ p) ∨ q)
⇒ S : (~ p) ∨ q
⇒ S : p ⇒ q
So, negation of S will be ~ (p ⇒ q)
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Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations