Respuesta :
Answer: a) FALSE b) FALSE
Step-by-step explanation:
a) For the given proposition p ∧ ¬(q ∨ s) you can solve first (q v s)
q v s is true if either q is true or s is true or both. It is only false if both q and s are false. So, the proposition (q v s) is true because q is true.
Now you can solve the negation: ¬(q ∨ s)
As we know, (q v s) is true then its negation ¬(q ∨ s) is false.
p ∧ ¬(q ∨ s) should be true when both p and ¬(q ∨ s) are true, and false otherwise. So, the proposition is false because p is true and ¬(q ∨ s) is false.
b) For the given proposition ¬(q ∧ p ∧ ¬s)
You can rewrite the expression as: ¬[q ∧ (p ∧ ¬s) ] to solve first each part of the propositions in parenthesis.
The negation of s: ¬s is true because s is false
Now, you can solve (p ∧ ¬s) which is true because both p and ¬s are true.
To continue, you have to solve (q ∧ p ∧ ¬s) which is true because both q and (p ∧ ¬s) are true.
To finish, the negation: ¬(q ∧ p ∧ ¬s) is false.
