A. For each of the following pairs of symbolic sentences: (i) Does the first logically imply...

  

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A. For each of the following pairs of symbolic sentences: (i) Does the first logically imply the second? (ii) Does the second logically imply the first? (iii) Are the two sentences logically equivalent? Produce truth tables to verify your answers in each case. 1. ~(PQ): ~P+Q 2. (PQ) &~(P&Q): ~P+Q 3. P&Q: P Q 4. P→Q: Q→ P B. Indicate whether the following arguments are valid or invalid and produce a truth table that verifies your claim: 5. (PQ)→ R; ~R/P 6. (PQ) & R; (R+P) /Q 7. (PQ)→ R; RP/~P & R 8. P & (QR); Q ~P; RQ;~Q→ R/Q A. For each of the following pairs of symbolic sentences: (i) Does the first logically imply the second? (ii) Does the second logically imply the first? (iii) Are the two sentences logically equivalent? Produce truth tables to verify your answers in each case. 1. ~(PQ): ~P+Q 2. (PQ) &~(P&Q): ~P+Q 3. P&Q: P Q 4. P→Q: Q→ P B. Indicate whether the following arguments are valid or invalid and produce a truth table that verifies your claim: 5. (PQ)→ R; ~R/P 6. (PQ) & R; (R+P) /Q 7. (PQ)→ R; RP/~P & R 8. P & (QR); Q ~P; RQ;~Q→ R/Q