Which, If Any, of the Following Proofs Are Correct Demonstrations

question 57

Multiple Choice

Which, if any, of the following proofs are correct demonstrations of the validity of this argument? $\begin{array}{l}\frac { ( P \cdot Q ) \cdot ( R \vee S ) } { Q }\\\text { Proof } 1\\\begin{array} { l l l } ( 1 ) ( P \cdot Q ) \cdot ( R \vee S ) & / Q & \text { Premise/Conclusion } \\\text { (2) } P \cdot Q & & 1 \mathrm { Simp } \\\text { (3) } R \vee S & & 1 \mathrm { Simp } \\\text { (4) } P & & 2 \mathrm { Simp } \\\text { (5) } Q & & 2 \mathrm { Simp } \\\text { Proof } 2 & & \\\text { (1) } ( \mathrm { P } \cdot \mathrm { Q } ) \cdot ( \mathrm { R } \vee \mathrm { S } ) & / \mathrm { Q } & \text { Premise/Conclusion } \\\text { (2) } P \cdot Q & & 1 \mathrm { Simp } \\\text { (3) } Q & & 2 \mathrm { Simp }\end{array}\end{array}$

• A)Proof 1
• B)Proof 2
• C)Proofs 1 and 2
• D)Neither proof
• E)Not enough information is provided because proofs are incomplete.

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