Let p :2 is a prime number
q : cos `30^@=1/2`
r:`sec^2x+tan^2x=1`
s=`sqrt7` is an irrational number
`u:pi^2` is greater than 10.
The truth values of `pvv~s and ~qvv~u` are, respectively, opposite to the values of

Options

A. (a)`pvvr,q^^s`
B. (b)`q^^s,~p^^u`
C. (c) `~pvvr,q^^~r`
D. (d) `~pvvu,r^^s`

Answer

To solve the problem, we need to evaluate the truth values of the given statements and then determine the truth values of the expressions \( p \lor \neg s \) and \( \neg q \lor \neg u \).

### Step 1: Determine the truth values of each statement

1. **Statement p**: "2 is a prime number."
- Truth value: **True** (T)

2. **Statement q**: "cos 30° = 1/2."
- Truth value: **False** (F) (The correct value is cos 30° = √3/2)

3. **Statement r**: "sec²x + tan²x = 1."
- Truth value: **False** (F) (The correct identity is sec²x = 1 + tan²x)

4. **Statement s**: "√7 is an irrational number."
- Truth value: **True** (T)

5. **Statement u**: "π² is greater than 10."
- Truth value: **False** (F) (Since π² ≈ 9.87, which is less than 10)

### Step 2: Evaluate the expressions

1. **Expression \( p \lor \neg s \)**:
- \( \neg s \): Since \( s \) is True, \( \neg s \) is False.
- Thus, \( p \lor \neg s \) = T or F = **True** (T).

2. **Expression \( \neg q \lor \neg u \)**:
- \( \neg q \): Since \( q \) is False, \( \neg q \) is True.
- \( \neg u \): Since \( u \) is False, \( \neg u \) is True.
- Thus, \( \neg q \lor \neg u \) = T or T = **True** (T).

### Step 3: Determine the opposite truth values

- The truth values of \( p \lor \neg s \) and \( \neg q \lor \neg u \) are both True (T).
- The opposite truth values would be **False (F)** for both expressions.

### Conclusion

The truth values of \( p \lor \neg s \) and \( \neg q \lor \neg u \) are both opposite to the values of **False (F)**.