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:

Options

A. (a) `(F,F)`
B. (b) `(F,T)`
C. (c) `(T,F)`
D. (d) `(T,T)`

Explanation

To solve the problem, we need to analyze the two statements P and Q, find their truth values, and then determine the truth values of their contrapositives.

### Step 1: Analyze Statement P
Statement P: "If 7 is an odd number, then 7 is divisible by 2."

- **Truth Value of P**:
- The first part "7 is an odd number" is true.
- The second part "7 is divisible by 2" is false.
- A true statement cannot imply a false statement, so P is false.

### Step 2: Find the Contrapositive of P
The contrapositive of a statement "If A, then B" is "If not B, then not A."

- For P:
- A = "7 is an odd number" (True)
- B = "7 is divisible by 2" (False)

- Contrapositive of P: "If 7 is not divisible by 2, then 7 is not an odd number."
- Here, "7 is not divisible by 2" is true (since 7 is odd).
- "7 is not an odd number" is false.

- **Truth Value of Contrapositive of P (V1)**: Since a true statement cannot imply a false statement, V1 is false (F).

### Step 3: Analyze Statement Q
Statement Q: "If 7 is a prime number, then 7 is an odd number."

- **Truth Value of Q**:
- The first part "7 is a prime number" is true.
- The second part "7 is an odd number" is also true.
- A true statement implies another true statement, so Q is true.

### Step 4: Find the Contrapositive of Q
- For Q:
- A = "7 is a prime number" (True)
- B = "7 is an odd number" (True)

- Contrapositive of Q: "If 7 is not an odd number, then 7 is not a prime number."
- Here, "7 is not an odd number" is false (since 7 is odd).
- "7 is not a prime number" is also false (since 7 is prime).

- **Truth Value of Contrapositive of Q (V2)**: Since a false statement cannot imply another false statement, V2 is true (T).

### Step 5: Form the Ordered Pair
Now we have:
- V1 = F (truth value of the contrapositive of P)
- V2 = T (truth value of the contrapositive of Q)

Thus, the ordered pair (V1, V2) is (F, T).

### Final Answer
The ordered pair (V1, V2) equals (F, T).

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