Question
If the invitations are printed on cream paper, then the writing is pink.
Question
Which statement must also be true?
Answer options with 4 options
A.
If the writing is pink, then the invitations are printed on cream paper.
B.
If the invitations are printed on cream paper, then the writing is not pink.
C.
If the writing is not pink, then the invitations are not printed on cream paper.
D.
If the invitations are not printed on cream paper, then the writing is not pink.
Question
Which statement must also be true?
Answer options with 4 options
A.
If the writing is pink, then the invitations are printed on cream paper.
B.
If the invitations are printed on cream paper, then the writing is not pink.
C.
If the writing is not pink, then the invitations are not printed on cream paper.
D.
If the invitations are not printed on cream paper, then the writing is not pink.
Answers
GPT-4o mini
The original statement is "If the invitations are printed on cream paper, then the writing is pink." This can be expressed in a logical format as:
- If P (invitations are printed on cream paper), then Q (the writing is pink).
The statement implies a conditional relationship, but it does not assert that the only condition for the writing to be pink is that the invitations are printed on cream paper. Therefore, we need to analyze each of the provided options to determine which must be true.
A. If the writing is pink, then the invitations are printed on cream paper.
- This cannot be concluded from the original statement, because there can be other scenarios where the writing is pink for other reasons. So this is not necessarily true.
B. If the invitations are printed on cream paper, then the writing is not pink.
- This contradicts the original statement, so it is certainly not true.
C. If the writing is not pink, then the invitations are not printed on cream paper.
- This is the contrapositive of the original statement and is logically equivalent to it. Therefore, this must be true.
D. If the invitations are not printed on cream paper, then the writing is not pink.
- This is not necessarily true because there could be cases where the writing is pink even if the invitations are not printed on cream paper.
From this analysis, the only statement that must also be true is option:
**C. If the writing is not pink, then the invitations are not printed on cream paper.**
- If P (invitations are printed on cream paper), then Q (the writing is pink).
The statement implies a conditional relationship, but it does not assert that the only condition for the writing to be pink is that the invitations are printed on cream paper. Therefore, we need to analyze each of the provided options to determine which must be true.
A. If the writing is pink, then the invitations are printed on cream paper.
- This cannot be concluded from the original statement, because there can be other scenarios where the writing is pink for other reasons. So this is not necessarily true.
B. If the invitations are printed on cream paper, then the writing is not pink.
- This contradicts the original statement, so it is certainly not true.
C. If the writing is not pink, then the invitations are not printed on cream paper.
- This is the contrapositive of the original statement and is logically equivalent to it. Therefore, this must be true.
D. If the invitations are not printed on cream paper, then the writing is not pink.
- This is not necessarily true because there could be cases where the writing is pink even if the invitations are not printed on cream paper.
From this analysis, the only statement that must also be true is option:
**C. If the writing is not pink, then the invitations are not printed on cream paper.**