Mathematical Re...

The moment of inertia of the plate about the $$x-$$axis is 

Negation of $$p \rightarrow ( p \vee \sim q )$$  is

The negation of $$q\vee \sim (p\wedge r)$$ is?

Dual of $$( p \rightarrow q ) \rightarrow r$$ is _________________.

Consider the following two statements :
P:   If 7 is odd number, then is divisible by $$2$$.
Q:   If 7 is a prime number, Then is an odd number.
If $${ V }_{ 1 }$$ is the value of the contra-positive of $$p$$ and $${ V }_{ 2 }$$ Is the truth value of contra-positive of Q, then the orders pair $$({ V }_{ 1 },{ V }_{ 2 })$$ equals :

P: he studies hard, q: he will get good marks. The symbolic form of " If he studies hard then he will get good marks "is_____

Negation of compound proposition : If the examination is difficult, then I shall pass if I study hard

The cost of an article including the sales tax is $$Rs\ .616$$. The rate of sales tax is $$10\%$$,if the shopkeeper has made a profit of $$12\%$$ , then the cost price of the article is?

Consider the following statement
p:you want to success
q:you will find a away,
then the negation of $$\sim \left( p\ \nu\ q \right) $$

If $$p, q, r$$ are three propositions, then the negation of $$p\rightarrow (q\wedge r)$$ is logically equivalent to