Consider the following statements :
p: It rains today
q: I go to school
r: I Shall meet any friends
s: I shall go for a movie
Then which of the following proposition represents 'If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie .'?

Options

A. `~(p^^q) to (r^^s)`
B. `~(p^^~q) to (r^^s)`
C. `~(p^^q) to (rvvs)`
D. None of these

Explanation

To solve the problem, we need to translate the given statement into logical symbols using the provided propositions.

### Step-by-Step Solution:

1. **Identify the Propositions:**
- Let \( p \): It rains today.
- Let \( q \): I go to school.
- Let \( r \): I shall meet my friends.
- Let \( s \): I shall go for a movie.

2. **Negate the Propositions:**
- The negation of \( p \) (It does not rain today) is represented as \( \neg p \).
- The negation of \( q \) (I do not go to school) is represented as \( \neg q \).

3. **Combine the Negations with OR:**
- The phrase "if it does not rain or if I do not go to school" translates to \( \neg p \lor \neg q \).

4. **Combine the Outcomes with AND:**
- The phrase "then I shall meet my friends and go for a movie" translates to \( r \land s \).

5. **Construct the Final Proposition:**
- The entire statement "If it does not rain or if I do not go to school, then I shall meet my friends and go for a movie" can be represented as:
\[ (\neg p \lor \neg q) \rightarrow (r \land s) \]

### Final Answer:
The proposition representing the statement is:
\[ (\neg p \lor \neg q) \rightarrow (r \land s) \]