In the scenario you provided, the transaction that would specifically affect the liability account is:
Supplies are purchased, on account.
When supplies are purchased on account, it means the business has incurred a liability because it owes money to the supplier for those supplies. This would increase the supplies account (an asset) and also increase accounts payable (a liability) on the balance sheet.
Let's briefly review how the other transactions affect accounts:
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Monthly rent is paid: This transaction would decrease cash (an asset) and also decrease rent payable (a liability, if any existed). If rent is not previously owed, then it's just an expense.
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The owner contributes cash to a business start-up: This transaction increases cash (an asset) and increases the owner's equity, not liabilities.
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Customer payments toward accounts receivable are collected: This would increase cash (an asset) and decrease accounts receivable (also an asset), but it does not affect liabilities.
So, the purchase of supplies on account is the only transaction listed that directly increases liabilities.