A financial regulatory board has issued a new set of auditing standards. Below are four ru… — LSAT

A financial regulatory board has issued a new set of auditing standards. Below are four rules extracted from these standards. Match each English regulatory rule to its accurate formal logical diagram.

Use the following variables for your diagramming:
$A$ : The audit is approved
$R$ : The receipts are verified
$L$ : The ledger is balanced
$D$ : Discrepancies are reported

No audit is approved without both the receipts being verified and the ledger being balanced. $A \rightarrow (R \land L)$
The ledger is balanced if the audit is approved, unless discrepancies are reported. $A \rightarrow (L \lor D)$
The audit being approved requires the receipts to be verified, but the ledger being balanced is sufficient for the audit to be approved. $(A \rightarrow R) \land (L \rightarrow A)$
The audit is approved if, but only if, the ledger is balanced and no discrepancies are reported. $A \leftrightarrow (L \land \neg D)$

Cevap

The correct matches are:
'No audit is approved without both...' matches with

A \rightarrow (R \land L)

'The ledger is balanced if the audit is approved, unless...' matches with

A \rightarrow (L \lor D)

'The audit being approved requires the receipts...' matches with

(A \rightarrow R) \land (L \rightarrow A)

'The audit is approved if, but only if...' matches with

A \leftrightarrow (L \land \neg D)

Each statement successfully maps English syntactic cues to their formal propositional logic equivalents. Mastering the nuances of words like 'unless', 'only if', and 'requires' ensures you avoid illegal reversals or negations in deduction chains.

Adım Adım Çözüm

Analyze the first statement for necessary conditions.

Translates 'No X without Y' to X -> Y, resulting in A -> (R AND L).

The 'without' modifier establishes that the absence of R and L precludes A, meaning A firmly implies their presence.

Deconstruct the 'unless' clause in the second statement.

Translates to ~D -> (A -> L), which is logically equivalent to A -> (L OR D).

'Unless' negates the following condition to form the sufficient trigger. Distributing this across the nested conditional yields an 'OR' relationship on the necessary side.

Split the third statement into its 'requires' and 'sufficient' components.

Yields two separate conditionals: A -> R and L -> A.

The sentence explicitly divides the relationship between R being necessary for A, and L being sufficient to guarantee A.

Identify the biconditional indicator in the fourth statement.

Translates 'if, but only if' to a two-way arrow, resulting in A <-> (L AND ~D).

Biconditionals indicate that both sides of the relationship are simultaneously necessary and sufficient for each other.

Anahtar Kavram

Accurate formal logical translation of complex English indicators ('unless', 'no X without Y', 'requires', 'sufficient', 'if, but only if').

Tahmini Süre:2m 30s

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