Final answer:
The English proposition 'You can see the movie if you are over 18 years old or you have the permission of a parent.' can be translated into symbolic form as 'Q v R > P,' where Q represents being over 18 years old, R represents having parental permission, and P represents seeing the movie.
Step-by-step explanation:
To translate the English proposition "You can see the movie if you are over 18 years old or you have the permission of a parent." into symbolic form, we will use logical symbols to represent the different components of the statement. In formal logic, propositions are often represented by capital letters (for example, P, Q, R, etc.), and logical connectives are used to combine these propositions. Let's define the following:
P: You can see the movie.
Q: You are over 18 years old.
R: You have the permission of a parent.
The proposition contains a conditional statement, which can be represented by '>,' meaning 'if... then...' and a disjunction, represented by 'v,' meaning 'or.' The statement 'You can see the movie if you are over 18 years old or you have the permission of a parent' can thus be translated into the following symbolic form:
Q v R > P
This reads as "If Q (you are over 18 years old) or R (you have the permission of a parent), then P (you can see the movie)." The use of the disjunction 'v' implies that either of the conditions being true is sufficient to make the conclusion true, according to the rules of logical deduction. This relates to the concept of noncontradiction where if one part of the 'or' statement is false, the other must be true for the entire conditional statement to hold.