Mathematical Re...

If statement $$(p\rightarrow q)\rightarrow (q\rightarrow r)$$ is false, then truth values of statements $$p,q,r$$ respectively, can be :

$$p \wedge ( q \vee \sim p ) =?$$

Negation of $$(\sim p\rightarrow q)$$ is ________________.

Consider the statement "if it is raining, then sky is not filled with clouds which among the Q 7 following is true

The statement $$P \rightarrow ( q \vee r )$$ is not equivalent to

The false statement in the following is

Consider the following statements
$$P:$$Suman is brilliant
$$Q:$$Suman is rich
$$R:$$Suman is honest.
The negative of the statement."Suman is brilliant and dishonest, if and only if Suman is rich" can be expressed as

The negation of $$p\wedge \left( q \rightarrow\ r \right)$$ is

Consider the following two statements: $$P:$$ if $$7$$ is an odd number, then $$7$$ is divisible by $$2$$.$$Q:$$ if $$7$$ is a prime number, then $$7$$ is an odd number If $$V_{1}$$ is the truth value of the contrapositive of $$P$$ and $$V_{2}$$ is the truth value of contrapositive of $$Q$$. Then the ordered pair $$\left(V_{1},V_{2}\right)$$ equals:

Negation of $$p \to \left( {p \vee  \sim q} \right)$$ is