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12 Nov 2024, 03:53
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1: whether or not
2: only if
Football matches between Fancy Club and Dare Devil never end in a tie whenever Louis Jr. plays for Fancy Club. However, Fancy Club has won against Dare Devil regardless of whether Louis Jr. played for the team.
Statements: Fancy Club has won matches against Dare Devil __1__ Louis Jr. has played in those matches. Furthermore, matches between Fancy Club and Dare Devil end in a tie __2__ Louis Jr. has not played for Fancy Club in those matches.
Select for 1 and for 2 the options that complete the statement so that it most accurately reflects the information provided. Make only two selections, one in each column. Make only two selections, one in each column.
Statements: Fancy Club has won matches against Dare Devil __1__ Louis Jr. has played in those matches. Furthermore, matches between Fancy Club and Dare Devil end in a tie __2__ Louis Jr. has not played for Fancy Club in those matches.
Select for 1 and for 2 the options that complete the statement so that it most accurately reflects the information provided. Make only two selections, one in each column. Make only two selections, one in each column.
| 1 | 2 | |
| if | ||
| only if | ||
| whether or not | ||
| unless | ||
| or |
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Official Answer
1: whether or not
2: only if
12 Nov 2024, 03:53
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Official Solution:
Since “whether Louis Jr. has played” means the same as “whether or not Louis Jr. has played,” the first statement is logically equivalent to “whether or not Louis Jr. has played, Fancy Club has won matches against Dare Devil.” This is logically equivalent to “Fancy Club has won matches against Dare Devil, whether or not Louis Jr. has played,” which corresponds to the selection whether or not.
To see why each of the other options gives a less accurate paraphrase:
• If: This gives a statement logically equivalent to “if Louis Jr. has played, then Fancy Club has won matches against Dare Devil,” which doesn’t include the provision that Fancy Club has won when Louis Jr. has not played. Hence, this creates a conditional relationship where Fancy Club's win depends on Louis Jr. playing, which is incorrect since Fancy Club wins regardless of his participation.
• Only if: This gives a statement logically equivalent to “Fancy Club has won matches against Dare Devil only if Louis Jr. has played,” which doesn’t allow for Fancy Club's wins when Louis Jr. has not played, which directly contradicts the information.
• Unless: This gives a statement logically equivalent to “Fancy Club has won matches against Dare Devil unless Louis Jr. has played,” (so this implies Fancy Club's wins against Dare Devil occur only when Louis Jr. has not played.) which doesn’t include the provision that Fancy Club has won when Louis Jr. has played.
• Or: This gives a statement logically equivalent to “Fancy Club has won matches against Dare Devil or Louis Jr. has played,” which doesn’t include the provision that Fancy Club has won when Louis Jr. has played.
Thus, the correct selection for the first blank is "whether or not."
The statement specifies that “matches between Fancy Club and Dare Devil never end in a tie whenever Louis Jr. plays for Fancy Club.” Since this means that if a match ends in a tie, Louis Jr. must not have played for Fancy Club, and a statement of the form “if a match ends in a tie, then Louis Jr. has not played” is logically equivalent to “matches between Fancy Club and Dare Devil end in a tie only if Louis Jr. has not played for Fancy Club in those matches,” it follows that the statement is logically equivalent to saying that “matches between Fancy Club and Dare Devil end in a tie only if Louis Jr. has not played for Fancy Club in those matches.”
To see why each of the other options gives a less accurate paraphrase:
• If: This gives a statement logically equivalent to “if Louis Jr. has not played for Fancy Club, then matches between Fancy Club and Dare Devil end in a tie.” This reverses the necessary condition by making Louis Jr.’s absence a sufficient condition for a tie, which is not implied by the original statement and is therefore not a paraphrase.
• Whether or not: This gives a statement logically equivalent to “matches between Fancy Club and Dare Devil end in a tie whether or not Louis Jr. has played for Fancy Club.” This removes the dependence on Louis Jr.’s participation, contradicting the original statement, which specifies that a tie can occur only if Louis Jr. has not played for Fancy Club. Therefore, it is not a paraphrase.
• Unless: The selection unless gives a statement logically equivalent to “matches between Fancy Club and Dare Devil end in a tie unless Louis Jr. has not played for Fancy Club in those matches.” This means:
- If Louis Jr. has played for Fancy Club, then matches between Fancy Club and Dare Devil do not end in a tie.
- If Louis Jr. has not played for Fancy Club, then matches between Fancy Club and Dare Devil do end in a tie.
This incorrectly implies that Louis Jr.’s absence is a sufficient condition for a tie. The original statement specifies that a tie can occur only if Louis Jr. has not played, but it does not guarantee a tie in his absence. Thus, the selection unless is not a paraphrase.
• Or: This gives a statement logically equivalent to “matches between Fancy Club and Dare Devil end in a tie, or Louis Jr. has not played for Fancy Club.” This does not establish the necessary condition for a tie because it suggests that either a tie occurs or Louis Jr. has not played, without linking the two in the required conditional relationship. Furthermore, the statement breaks under scenarios where Fancy Club or Dare Devil wins and Louis Jr. plays, as neither condition of the "or" statement would hold true. Therefore, it is not a paraphrase.
Thus, the correct selection for the first blank is "only if."
Correct answer:
1 "whether or not"
2 "only if"
Bunuel
Since “whether Louis Jr. has played” means the same as “whether or not Louis Jr. has played,” the first statement is logically equivalent to “whether or not Louis Jr. has played, Fancy Club has won matches against Dare Devil.” This is logically equivalent to “Fancy Club has won matches against Dare Devil, whether or not Louis Jr. has played,” which corresponds to the selection whether or not.
To see why each of the other options gives a less accurate paraphrase:
• If: This gives a statement logically equivalent to “if Louis Jr. has played, then Fancy Club has won matches against Dare Devil,” which doesn’t include the provision that Fancy Club has won when Louis Jr. has not played. Hence, this creates a conditional relationship where Fancy Club's win depends on Louis Jr. playing, which is incorrect since Fancy Club wins regardless of his participation.
• Only if: This gives a statement logically equivalent to “Fancy Club has won matches against Dare Devil only if Louis Jr. has played,” which doesn’t allow for Fancy Club's wins when Louis Jr. has not played, which directly contradicts the information.
• Unless: This gives a statement logically equivalent to “Fancy Club has won matches against Dare Devil unless Louis Jr. has played,” (so this implies Fancy Club's wins against Dare Devil occur only when Louis Jr. has not played.) which doesn’t include the provision that Fancy Club has won when Louis Jr. has played.
• Or: This gives a statement logically equivalent to “Fancy Club has won matches against Dare Devil or Louis Jr. has played,” which doesn’t include the provision that Fancy Club has won when Louis Jr. has played.
Thus, the correct selection for the first blank is "whether or not."
The statement specifies that “matches between Fancy Club and Dare Devil never end in a tie whenever Louis Jr. plays for Fancy Club.” Since this means that if a match ends in a tie, Louis Jr. must not have played for Fancy Club, and a statement of the form “if a match ends in a tie, then Louis Jr. has not played” is logically equivalent to “matches between Fancy Club and Dare Devil end in a tie only if Louis Jr. has not played for Fancy Club in those matches,” it follows that the statement is logically equivalent to saying that “matches between Fancy Club and Dare Devil end in a tie only if Louis Jr. has not played for Fancy Club in those matches.”
To see why each of the other options gives a less accurate paraphrase:
• If: This gives a statement logically equivalent to “if Louis Jr. has not played for Fancy Club, then matches between Fancy Club and Dare Devil end in a tie.” This reverses the necessary condition by making Louis Jr.’s absence a sufficient condition for a tie, which is not implied by the original statement and is therefore not a paraphrase.
• Whether or not: This gives a statement logically equivalent to “matches between Fancy Club and Dare Devil end in a tie whether or not Louis Jr. has played for Fancy Club.” This removes the dependence on Louis Jr.’s participation, contradicting the original statement, which specifies that a tie can occur only if Louis Jr. has not played for Fancy Club. Therefore, it is not a paraphrase.
• Unless: The selection unless gives a statement logically equivalent to “matches between Fancy Club and Dare Devil end in a tie unless Louis Jr. has not played for Fancy Club in those matches.” This means:
- If Louis Jr. has played for Fancy Club, then matches between Fancy Club and Dare Devil do not end in a tie.
- If Louis Jr. has not played for Fancy Club, then matches between Fancy Club and Dare Devil do end in a tie.
This incorrectly implies that Louis Jr.’s absence is a sufficient condition for a tie. The original statement specifies that a tie can occur only if Louis Jr. has not played, but it does not guarantee a tie in his absence. Thus, the selection unless is not a paraphrase.
• Or: This gives a statement logically equivalent to “matches between Fancy Club and Dare Devil end in a tie, or Louis Jr. has not played for Fancy Club.” This does not establish the necessary condition for a tie because it suggests that either a tie occurs or Louis Jr. has not played, without linking the two in the required conditional relationship. Furthermore, the statement breaks under scenarios where Fancy Club or Dare Devil wins and Louis Jr. plays, as neither condition of the "or" statement would hold true. Therefore, it is not a paraphrase.
Thus, the correct selection for the first blank is "only if."
Correct answer:
1 "whether or not"
2 "only if"
