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

First, we recall the standard logical rule: for any implication of the form $$A \rightarrow B$$ the contrapositive is the statement $$\lnot B \rightarrow \lnot A$$ and both have exactly the same truth value. We will apply this rule separately to the two given statements $$P$$ and $$Q$$, and then determine the ordered pair of their truth values.

We have the statement $$P$$:

$$P:\qquad$$ If $$7$$ is an odd number, then $$7$$ is divisible by $$2.$$

For $$P$$ the antecedent (the “if” part) is

$$A:\;7\text{ is an odd number},$$

and the consequent (the “then” part) is

$$B:\;7\text{ is divisible by }2.$$

Using the contrapositive rule, the contrapositive of $$P$$ is

$$\lnot B \rightarrow \lnot A.$$

Writing it out in words:

If $$7$$ is \emph{not $$divisible by }2,$$ then $$7$$ is \emph{not $$an odd number}.$$

Now, we determine the truth value of this contrapositive:

• The statement “7 is not divisible by 2” is true because 7 divided by 2 does not give an integer quotient.
• The statement “7 is not an odd number” is false because 7 is indeed odd.

In a conditional $$X \rightarrow Y,$$ if the antecedent $$X$$ is true and the consequent $$Y$$ is false, the whole conditional is false. Therefore, the contrapositive of $$P$$ is false. We denote this by

$$V_1 = F.$$

Next, we analyze the statement $$Q$$:

$$Q:\qquad$$ If $$7$$ is a prime number, then $$7$$ is an odd number $$.$$

Here, the antecedent is

$$C:\;7\text{ is a prime number},$$

and the consequent is

$$D:\;7\text{ is an odd number}.$$

The contrapositive of $$Q$$ is

$$\lnot D \rightarrow \lnot C,$$

that is,

If $$7$$ is \emph{not $$an odd number, then }7$$ is \emph{not $$a prime number}.$$

We check its truth value:

• The antecedent “7 is not an odd number” is false because 7 is odd.
• In material implication, whenever the antecedent is false, the entire conditional statement is automatically true, regardless of the consequent.

Hence the contrapositive of $$Q$$ is true, and we write

$$V_2 = T.$$

Collecting the two truth values, we obtain the ordered pair

$$(V_1, V_2) = (F, T).$$

This matches Option A.

Hence, the correct answer is Option A.