10. Construir las tablas de verdad de las siguientes fórmulas proposicionales. a) (p ∨ q)→ p b) (p ∧ q)→ p c) (p ∧ q)→ (q ∧ p) d) (p ∧ q)→ (q ∨ p)...

a) | p | q | p ∨ q | (p ∨ q) → p | |---|---|-------|--------------| | V | V | V | V | | V | F | V | V | | F | V | V | F | | F | F | F | V | b) | p | q | p ∧ q | (p ∧ q) → p | |---|---|-------|--------------| | V | V | V | V | | V | F | F | V | | F | V | F | F | | F | F | F | V | c) | p | q | p ∧ q | q ∧ p | (p ∧ q) → (q ∧ p) | |---|---|-------|-------|------------------| | V | V | V | V | V | | V | F | F | F | V | | F | V | F | F | V | | F | F | F | F | V | d) | p | q | p ∧ q | q ∨ p | (p ∧ q) → (q ∨ p) | |---|---|-------|-------|------------------| | V | V | V | V | V | | V | F | F | V | V | | F | V | F | V | V | | F | F | F | F | V | e) | p | q | p ∧ q | p → (p ∧ q) | |---|---|-------|--------------| | V | V | V | V | | V | F | F | F | | F | V | F | F | | F | F | F | F | f) | p | q | p ∨ q | p ∨ q → p | |---|---|-------|--------------| | V | V | V | V | | V | F | V | V | | F | V | V | F | | F | F | F | V | g) | p | p ∧ p | p → (p ∧ p) | |---|-------|--------------| | V | V | V | | F | F | V | h) | p | q | r | p ∧ q | (p ∧ q) ∨ r | (p ∧ q) ∨ r → r | |---|---|---|-------|--------------|------------------| | V | V | V | V | V | V | | V | V | F | V | V | F | | V | F | V | F | V | V | | V | F | F | F | F | V | | F | V | V | F | V | V | | F | V | F | F | F | V | | F | F | V | F | V | V | | F | F | F | F | F | V | i) | p | q | r | p ∧ q | q ∨ r | (p ∧ q) → (q ∨ r) | |---|---|---|-------|-------|------------------| | V | V | V | V | V | V | | V | V | F | V | V | V | | V | F | V | F | V | V | | V | F | F | F | F | V | | F | V | V | F | V | V | | F | V | F | F | F | V | | F | F | V | F | V | V | | F | F | F | F | F | V | j) | p | q | p → q | q → p | (p → q) → (q → p) | |---|---|-------|-------|------------------| | V | V | V | V | V | | V | F | F | V | V | | F | V | V | F | F | | F | F | V | V | V | k) | p | q | p → q | q → p | (p → q) ∨ (q → p) | |---|---|-------|-------|------------------| | V | V | V | V | V | | V | F | F | V | V | | F | V | V | F | V | | F | F | V | V | V | l) | p | q | p ∨ q | (p ∨ q) ∧ p | |---|---|-------|--------------| | V | V | V | V | | V | F | V | V | | F | V | V | F | | F | F | F | F | m) | p | q | p → q | (p → q) → p | |---|---|-------|--------------| | V | V | V | V | | V | F | F | V | | F | V | V | F | | F | F | V | V | n) | p | q | (p → q) | ((p → q) → p) | (((p → q) → p) → p) | |---|---|---------|------------------|------------------------| | V | V | V | V | V | | V | F | F | V | V | | F | V | V | F | V | | F | F | V | V | V | ñ) | p | q | q → p | p → (q → p) | |---|---|-------|--------------| | V | V | V | V | | V | F | V | V | | F | V | F | V | | F | F | V | V | o) | p | q | r | q ∨ r | p → (q ∨ r) | |---|---|---|-------|--------------| | V | V | V | V | V | | V | V | F | V | V | | V | F | V | V | V | | V | F | F | F | F | | F | V | V | V | V | | F | V | F | V | V | | F | F | V | V | V | | F | F | F | F | V | p) | p | q | (p → q) | (¬p → ¬q) | (p → q) → (¬p → ¬q) | |---|---|---------|--------------|------------------------| | V | V | V | V | V | | V | F | F | V | V | | F | V | V | F | F | | F | F | V | V | V | q) | p | q | (p → q) | (¬q → ¬p) | (p → q) → (¬q → ¬p) | |---|---|---------|--------------|------------------------| | V | V | V | V | V | | V | F | F | F | V | | F | V | V | V | V | | F | F | V | V | V | r) | p | q | ¬(p ∧ q) | |---|---|--------------| | V | V | F | | V | F | V | | F | V | V | | F | F | V | s) | p | q | ¬(p ∧ q) | ¬(p ∧ q) → ¬p | |---|---|--------------|------------------| | V | V | F | F | | V | F | V | V | | F | V | V | V | | F | F | V | V | t) | p | q | ¬(p ∨ q) | ¬(p ∨ q) → ¬p | |---|---|--------------|------------------| | V | V | F | F | | V | F | F | F | | F | V | F | V | | F | F | V | V | u) | p | q | r | p ∨ q | (p ∨ q) ∨ r | |---|---|---|-------|--------------| | V | V | V | V | V | | V | V | F | V | V | | V | F | V | V | V | | V | F | F | V | V | | F | V | V | V | V | | F | V | F | V | V | | F | F | V | F | V | | F | F | F | F | F | v) | p | q | r | p ∨ q | (p ∨ q) ∨ r | |---|---|---|-------|--------------| | V | V | V | V | V | | V | V | F | V | V | | V | F | V | V | V | | V | F | F | V | V | | F | V | V | V | V | | F | V | F | V | V | | F | F | V | F | V | | F | F | F | F | F | w) | p | q | ¬(p ∨ q) | (¬(p ∨ q)) ∧ r | |---|---|--------------|------------------| | V | V | F | r | | V | F | F | r | | F | V | F | r | | F | F | V | F | x) | p | q | (p ↔ q) | (p → q) | (p ↔ q) → (p → q) | |---|---|---------|--------------|------------------------| | V | V | V | V | V | | V | F | F | F | V | | F | V | F | V | F | | F | F | V | V | V | y) | p | q | (p → q) | (q → p) | (p → q) → (p ↔ q) | |---|---|---------|--------------|------------------------| | V | V | V | V | V | | V | F | F | V | F | | F | V | V | F | F | | F | F | V | V | V | z) | p | q | (p ↔ q) | p ∧ q | (p ↔ q) → (p ∧ q) | |---|---|---------|-------|------------------------| | V | V | V | V | V | | V | F | F | F | V | | F | V | F | F | V | | F | F | V | F | F |