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Mon 25 Jul, 2011 12:34 pm
Construct propositional natural deduction proofs for the following sequents and tautologies, including complete justification columns.
1. [(~M&R) &~P]&D, ~M->Q ⊢ QvT
[(BOTH ~M AND R) AND NOT P] AND D, IF NOT M THEN Q THUS Q OR T
1. | [(M&R) &~P]&D A
2. | ~M->Q A
2: ~[P v (QvZ)], (~ZvL) ->M ⊢ M
NOT (EITHER P OR ( Q OR Z)),(IF NOT Z OR L THEN M) THUS M
1. |[P v (QvZ)] A
2. | (~ZvL)->M A
3: PQ, (~PQ) (W&T), T(S~R) ⊢ R
IF P THEN Q, IF (EITHER NOT P OR Q) THEN W AND T, IF T THEN NOT (EITHER S OR NOT R) THUS R
1. | P Q A
2. |(~PQ) (W&T) A
3. | T ~ (Sv~R) A
4: ⊢ [(~PvL)&(~P vM) [P(L&M)]
IF BOTH (NOT P OR L) AND (IF NOT P OR M) THEN EITHER P OR (L AND M)
1. |
5: ├ (Q~Q) (P&~P)
THUS EITHER (Q OR NOT Q) OR ( P AND NOT P)
1. |