Question

1. \if the meeting is in brisbane, then we can see a movie or we can go to the concert.\

4a what is the statement in symbolic form?
let
p: the meeting is in brisbane.
q: we can see a movie.
r: we can go to the concert.
options:
a ((p rightarrow q) vee r)
b (p rightarrow (sim q vee sim r))
c (p leftrightarrow (q wedge r))
d (p rightarrow (q vee r))

Explanation:

The original statement is "If the meeting is in Brisbane, then we can see a movie or we can go to the concert." In symbolic logic, "if \( p \), then \( q \) or \( r \)" is represented as \( p \Rightarrow (q \vee r) \), where \( p \) is "The meeting is in Brisbane", \( q \) is "We can see a movie", and \( r \) is "We can go to the concert". Option A is \((p \Rightarrow q) \vee r\) which is not the correct structure. Option B has negations which are not in the original statement. Option C is a biconditional (\( \Leftrightarrow \)) which the original statement is not (it's a conditional, not an "if and only if"). So the correct symbolic form is \( p \Rightarrow (q \vee r) \), which is option D.

Answer:

D. \( p \Rightarrow (q \vee r) \)