Question:medium

If 
\( p \): It is raining today, 
\( q \): I go to school, 
\( r \): I shall meet my friends, 
and \( s \): I shall go for a movie, then which of the following 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?"

Show Hint

Use logical operators systematically to convert English statements into symbolic form.
Updated On: Jan 13, 2026
  • \( \neg (p \wedge q) \Rightarrow (r \wedge s) \)
  • \( \neg (p \wedge \neg q) \Rightarrow (r \wedge s) \)
  • \( \neg (p \wedge q) \Rightarrow (r \vee s) \)
  • None of these
Show Solution

The Correct Option is A

Solution and Explanation

The statement translates to: {"If it does not rain or I do not go to school, then I shall meet my friend and go for a movie."} The clause "does not rain or do not go to school" is represented as: \[ eg (p \wedge q) \] The clause "I shall meet my friend and go for a movie" is represented as: \[ r \wedge s \] Consequently, the logical expression is: \[ eg (p \wedge q) \Rightarrow (r \wedge s) \]
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