Discrete Mathematics 1.2 Concepts

p ↔ ¬¬p

double negation; equivalence

p —> q ↔ ¬p v q

implication; equivalence

¬(p ^ q) ↔ ¬p v ¬q / ¬(p v q) ↔ ¬p ^ ¬q

De Morgan’s laws; equivalence

p v q ↔ q v p / p ^ q ↔ q ^ p

commutativity; equivalence

p ^ (q ^ r) ↔ (p ^ q) ^ r / p v (q v r) ↔ (p v q) v r

associativity; equivalence

p}

q} —> p ^ q

conjunction; inference

p}

p —> q} —> q

modus ponens; inference

¬q}

p —> q} —> ¬p

modus tollens; inference

p ^ q —> p

simplification; inference

p —> p v q

addition; inference