( ( [(p/\q)/\r] \/ [(p/\q)/\~r]) \/~q ) -> s how can we simplify the compound statement? please help me I must do it until monday I can do up to three steps but ı dont know what it can continue
You might need to use the distributive law for disjunction and conjunction .
For example, (A/\B)\/(A/\~B) = A/\(B\/~B) = A
Additionally, A->B equals ~A\/B (ex.((A->B) <-> (~A\/B))).
After simplifying your formula, you might need to verify the result using a truth table.
Hello, lozgur!
Vagabond is absolutely correct.
I'll run though the steps and hope you know the reasons.
Simplify: .$\displaystyle \bigg\{\bigg[(p \wedge q \wedge r) \vee (p \wedge q \wedge \sim r)\bigg] \vee\sim q \bigg\} \to s $
Inside the brackets: .$\displaystyle (p \wedge q \wedge r) \vee (p \wedge q \:\wedge \sim r)$
"Factor": .$\displaystyle (p \wedge q) \wedge \underbrace{(r \:\vee \sim r)}$
. . . . . $\displaystyle = \;\underbrace{(p \wedge q) \quad\wedge\quad t}$
. . . . . $\displaystyle = \qquad\;\; p \wedge q$
The problem becomes: .$\displaystyle \bigg[(p \wedge q) \:\vee \sim q\bigg] \to s$
Distribute: . . . . $\displaystyle \bigg[(p \:\vee \sim q) \wedge (q \:\vee \sim q)\bigg] \to s$
. . . . . . . . . . . . . . . $\displaystyle \bigg[(p \:\vee \sim q) \wedge t\bigg] \to s $
. . . . . . . . . . . . . . . . . . $\displaystyle (p \:\vee \sim q) \to s$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
How far should we go? . . . There's no limit . . .
$\displaystyle (p \;\vee \sim q) \to s$
. . $\displaystyle \sim(p \;\vee \sim q) \vee s$
. . . $\displaystyle (\sim p \wedge q) \vee s$ . . . another answer
$\displaystyle (p \:\vee \sim q) \to s$
. . $\displaystyle (\sim q \vee p) \to s$
. . $\displaystyle (q \to p) \to s$ . . . and another
Question:
For each of these sets of premises, what relevant conclusion or conclu-
sions can be drawn? Explain the rules of inference used to obtain each
conclusion from premises.(a) "If I eat spicy foods, then I have strange dreams." "I have strange
dreams if there is thunder while I sleep." "I did not have strange
dreams."
(b) "I am dreaming or hallucinating." "I am not dreaming." "If I am
hallucinating, I see elephants running down the roads."
ı instaled this statement:
(a)
p:I eat spicy foods
q:I have strange dreams
r:there is thunder while I sleep
(p->q)/\(r->q)/\~q
do ı solve [(p->q)/\(r->q)/\~q] this statement for this question? ı dont understand what this question say