14. True or False? Aa Aa Use your knowledge of natural deduction in propositional logic and your knowledge of the rules of implication to determine which of the following statements are true. Place a check mark in the box beside each true statement. Simplification (Simp) allows you to obtain the left-hand conjunct of a conjunction on a separate and subsequent proof line. Constructive dilemma (CD) always yields a conditional proposition as its conclusion. Conjunction (Conj) allows you to add any proposition to a previous whole line using a wedge. You cannot apply more than one rule at a time on any line of a proof. If you are trying to prove a conjunction, you should consider obtaining it by addition (Add) after first proving each of the conjuncts independently You can apply the simplification (Simp) rule to a conjunction that is a component of a larger proposition. Conjunction allows you to conjoin with a dot any two propositions on previous proof lines. If you need to prove a disjunction, you should consider obtaining it by addition (Add) or constructive dilemma (CD). It is possible to obtain the proposition Z. (R O F) by the constructive dilemma (CD) rule. ? Constructive dilemma CD requires one premise that is the conjunction o two conditionals and a second disuntive premise whose disjuncts correspond to the antecedents of the conditionals in the first premise. 14. True or False? Aa Aa Use your knowledge of natural deduction in propositional logic and your knowledge of the rules of implication to determine which of the following statements are true. Place a check mark in the box beside each true statement. Simplification (Simp) allows you to obtain the left-hand conjunct of a conjunction on a separate and subsequent proof line. Constructive dilemma (CD) always yields a conditional proposition as its conclusion. Conjunction (Conj) allows you to add any proposition to a previous whole line using a wedge. You cannot apply more than one rule at a time on any line of a proof. If you are trying to prove a conjunction, you should consider obtaining it by addition (Add) after first proving each of the conjuncts independently You can apply the simplification (Simp) rule to a conjunction that is a component of a larger proposition. Conjunction allows you to conjoin with a dot any two propositions on previous proof lines. If you need to prove a disjunction, you should consider obtaining it by addition (Add) or constructive dilemma (CD). It is possible to obtain the proposition Z. (R O F) by the constructive dilemma (CD) rule. ? Constructive dilemma CD requires one premise that is the conjunction o two conditionals and a second disuntive premise whose disjuncts correspond to the antecedents of the conditionals in the first premise