## Question

###### And OrProof Techniques/Lemmas Better for cutting and Modus Ponens: From & and &->8, conclude 8_ Deduction: Assume 0, prove B, conclude &~8. paisting Equivalence: From u and >u conclude & iff B. Contrapositive: _8 > 7u iff (a^-8) iff &>8. Transitivity: From & >8 and 8 >Y, conclude 0-Y_ By Cases: From avB, &->Y and 8>Y, conclude Y By Contradiction: From u-B,and U->~B; conclude & _ Inconsistent: From 8 and ~B; conclude anything: Separating

And Or Proof Techniques/Lemmas Better for cutting and Modus Ponens: From & and &->8, conclude 8_ Deduction: Assume 0, prove B, conclude &~8. paisting Equivalence: From u and >u conclude & iff B. Contrapositive: _8 > 7u iff (a^-8) iff &>8. Transitivity: From & >8 and 8 >Y, conclude 0-Y_ By Cases: From avB, &->Y and 8>Y, conclude Y By Contradiction: From u-B,and U->~B; conclude & _ Inconsistent: From 8 and ~B; conclude anything: Separating And: From GAB, conclude & and B. Selecting Or: From uvf and ~0, conclude 8. Eval Building: From 0, &" B; conclude UAU ~(BAy), avy, Y->0, 83= Double Negation: From "U, conclude &. Add or remove at will: Excluded Middle: Uv-a and -(a^-a)_ Commutative: avf iff Bva and &^ iff BAa De Morgan's Law: (anB) iff ~uv-B Distributive: YA(avB) iff (YAa)V(YA8) and Yv(anB) iff (YVa)A(yvB)