Question

The disjunction of “I will go to the movie only if you come with me” is
A. I will go to the movies only if you will not come with me.
B. I will go to the movies and you come with me.
C. I will go to the movies if you come with me.
D. I will go to the movies or you can come with me.

Answer 1

Hint: We will break the given statement into two simple statements and then using the concept of disjunction of a statement that it is a compound statement which is written in the form p or q we will choose the disjunction from the above given options.
* A disjunction is a compound statement in logic formed by joining two simple statements by OR.
We write p OR q . It is also denoted by the sign \[\nu \] in between the two statements, i.e. p \[\nu \] q

Complete step-by-step answer:
We are given the statement “I will go to the movie only if you come with me”
We can break the above given compound sentence into two simple statements as “I will go to the movie” and “You come with me”.
Now let us assume
The statement “I will go to the movie” is p.
The statement “You come with me” is q.
From the definition of disjunction of a sentence we know it is of the form p OR q
So, substituting the simple statements in place of p and q we can write the disjunction as
“I will go to the movie” OR “You come with me”
Now we combine the statements to make one sentence.
“I will go to the movie or you can come with me.”

So, the correct answer is “Option D”.

Additional Information:
There are two types of disjunction, Inclusive and Exclusive.
An Inclusive disjunction complex statement is true when either or both of its propositions are true.
In Exclusive disjunction complex statements are true when one and only one of its constituent statements is true.
Also, the only way for a disjunction to be false is if both its constituents are false.

Note: Students are likely to get confused when two simple statements are not given separately and are given in a sentence form where there are adjoining words like if, and etc. Students are advised to break the sentence into two simple statements and then proceed.