Mathematical Re...

The negation of the boolean expression
$$\sim s\vee \left( \sim r\wedge s \right) $$ is equivalent to:

Negation of the statement:
$$\sqrt{5}$$ is an integer or $$5$$ is irrational is?

Consider the following three statements:
P : 5 is a prime number.
Q : 7 is a factor of 192.
R : L.C.M. of 5 and 7 is 35.
Then the truth value of which one of thefollowing statements is true ?

The negation of the statement: "If I become a teacher, then I will open a school" is

The contrapositive of the statement 'I go to school if it does not rain' is:

The negation of $$\sim s \vee (\sim r\wedge s)$$ is equivalent to

The contrapositive of the statement 'If I am not feeling well, then I will go to the doctor' is:

The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times"' 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 $$(V_{1}, V_{2})$$ equals:

The Boolean expression  $$( ( p \wedge q ) \vee ( p \vee \sim q ) ) \wedge ( \sim p \wedge \sim q )$$  is equivalent to :