Mathematical Re...

If p, q, r have truth values T, F, T respectively, then which of the following is $$\text{True}$$?

$$\sim [(\sim p) \wedge q]$$ is logically equivalent to

The contrapositive statement of statement "If x is prime number, then x is odd" is

Let
$$p:57$$ is an odd prime number
$$q:4$$ is a divisor of $$12$$
$$r:15$$ is the LCM of $$3$$ and $$5$$
be three simple logical statements. Which one of the following is true?

The converse of the contrapositive of the conditional $$p\rightarrow \sim q$$ is.

Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement.

If $$p\vee q$$ is true and $$p\wedge q$$ is false, then which of the following is not true?

Given are three positive integers $$a, b,$$ and $$c$$. Their greatest common divisor is $$D$$; their least common multiple is $$M$$. Then, which two of the following statements are true?
$$(1)$$ The product $$MD$$ cannot be less than $$abc$$
$$(2)$$ The product $$MD$$ cannot be greater than $$abc$$
$$(3)$$ $$MD$$ equals $$abc$$ if and only if $$a, b, c$$ are each prime
$$(4)$$ $$MD$$ equals $$abc$$ if and only if $$a, b, c$$ are relatively prime in pairs
(This means : no two have a common factor greater than $$1$$.)

Given the following six statements:
(1) All women are good drivers
(2) Some women are good drivers
(3) No men are good drivers
(4) All men are bad drivers
(5) At least one man is a bad driver 
(6) All men are good drivers.
The statement that negates statement (6) is:

Which one of the following statements is not true for the equation
$$i{ x }^{ 2 }-x+2i=0$$.
where $$i\equiv \sqrt { -1 } $$?