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**bee77** (a) ¬(p ∨ q ) and ¬p ∧ ¬q

for a the truth table

| p q | ¬(p ∨ q ) | ¬p ∧ ¬q |

| T F | F | F |

| T F | F | F |

| F T | F | F |

| F F | T | T |

We find that using a truth table for a) that ¬(p ∨ q ) and ¬p ∧ ¬q are logically equivalent using the definition of Conjunction ,Disjunction and Negation with Binary Operations on propositions .

de Morgan’s Law:¬(p ∨ q ) ≡ ¬p ∧ ¬q also holds true .

b) ¬ (p → q ) and p ∧ ¬q

for a the truth table

| p q |¬ (p → q) | p ∧ ¬q |

| T F | F | F |

| T F | T | T |

| F T | F | F |

| F F | F | F |

We find that using a truth table for b) that ¬ (p → q ) and p ∧ ¬q are logically equivalent using the definition of Conjunction ,Disjunction and Negation with Binary Operations on propositions .

de Morgan’s Law: ¬ (p → q )≡ p ∧ ¬q also holds true .

Is that correct ?