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d) Assume ⊥ occurs in a subproof of the main proof. The appearance of ⊥ in this subproof indicates that: 1. The premises of the main proof are mutually inconsistent. 2. The assumption of the subproof is a TT-contradiction. 3. One of the premises is the negation of the assumption of the subproof. 4. The premises of the main proof, together with the assumption of the subproof are mutually inconsistent. e) Recall that conjunction is idempotent, that is A ∧ A⇔A and commutative, that is A ∧ B⇔B ∧ A. Which of these properties h old of material conditional (→). 1. Idempotent and commutative 2. Idempotent and not commutative 3. Commutative but not idempotent 4. Neither idempotent nor commutative
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