If Bobby and Danny are selected in that order, Parvez and Santhi cannot be…
2024
If Bobby and Danny are selected in that order, Parvez and Santhi cannot be selected.
A. Parvez and Santhi are selected in that order.
B. Danny and Bobby are selected in that order.
C. Bobby and Danny are selected in that order.
D. Parvez and Santhi are not selected.
Which of the following combinations of the above four statements represents a logically valid pairing, based on the given statement?
- A.
BC
- B.
CD
- C.
BD
- D.
DB
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Concept: A statement of the form “If P, then Q” asserts a direct implication, P → Q. Among any set of listed statements, the only two-statement pairing that this rule itself ties together — and is therefore the valid, rule-consistent pairing — is P combined with Q, because P → Q means that whenever P holds, Q must follow. This identifies the rule's own antecedent-consequent link; it is not a claim that P and Q are simultaneously true in every case. Pairing two statements the rule never connects, or two statements that contradict each other, is never a valid, rule-consistent pairing — regardless of the order in which they are listed.
Application: The given rule is “If Bobby and Danny are selected in that order, then Parvez and Santhi cannot be selected.” Label the four listed statements as given: A — Parvez and Santhi selected in that order; B — Danny and Bobby selected in that order; C — Bobby and Danny selected in that order; D — Parvez and Santhi are not selected. So the rule is exactly C → D. Since the question asks which combination of these four statements is a valid, rule-consistent pairing, checking every offered combination against the rule:
Combination | What it pairs | Rule-consistent pairing? |
|---|---|---|
BC | Danny-and-Bobby in that order, together with Bobby-and-Danny in that order | No — these are two different orders of the same two people; both cannot hold at once |
CD | Bobby-and-Danny in that order, together with Parvez-and-Santhi not selected | Yes — this is the rule's own antecedent paired with its own consequent |
BD | Danny-and-Bobby in that order, together with Parvez-and-Santhi not selected | No — the rule never links Danny-and-Bobby's order to Parvez-and-Santhi's status |
DB | Parvez-and-Santhi not selected, together with Danny-and-Bobby in that order | No — the same two statements as above; reversing the listing order creates no new link |
Cross-check: Rewriting the rule the other way round — if Parvez and Santhi ARE selected, then Bobby and Danny cannot be selected in that order — still only ties the rule's own two statements to each other; it says nothing about Danny-and-Bobby's order. So among A, B, C, D, the only pairing the given rule itself ties together is its own antecedent with its own consequent.
Result: So among the four offered combinations, pairing “Bobby and Danny selected in that order” with “Parvez and Santhi are not selected” (CD) is the one that correctly represents the rule's own antecedent paired with its own consequent — the valid, rule-consistent pairing asked for.