(a)
¬(p∧(p→¬q))→¬p¬(p∧(¬p∨¬q))→¬p Implication¬((p∧¬p)∨(p∧¬q))→¬p Distributive ¬(F∨(p∧¬q))→¬p Identity ¬(p∧¬q)→¬p Absorption ¬¬(p∧¬q)∨¬p Implication (p∧¬q)∨¬p Negation (p∨¬p)∧(¬q∨¬p) Distributive T∧(¬q∨¬p) Identity(¬q∨¬p) Absorption
(b)
¬(q→¬p)→¬q¬¬(¬q∨¬p)∨¬q Implications (¬q∨¬p)∨¬q Double Negation (¬p∨¬q)∨¬q Commutative ¬p∨(¬q∨¬q) Associative ¬p∨¬q Idempotent Law¬q∨¬p Commutative
The are consistent by reasoning methods
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