Math Help - how can we simplify ? pfff:(

1. how can we simplify ? pfff:(

( ( [(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

2. 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.

3. Hello, lozgur!

Vagabond is absolutely correct.
I'll run though the steps and hope you know the reasons.

Simplify: . $\bigg\{\bigg[(p \wedge q \wedge r) \vee (p \wedge q \wedge \sim r)\bigg] \vee\sim q \bigg\} \to s$

Inside the brackets: . $(p \wedge q \wedge r) \vee (p \wedge q \:\wedge \sim r)$

"Factor": . $(p \wedge q) \wedge \underbrace{(r \:\vee \sim r)}$

. . . . . $= \;\underbrace{(p \wedge q) \quad\wedge\quad t}$

. . . . . $= \qquad\;\; p \wedge q$

The problem becomes: . $\bigg[(p \wedge q) \:\vee \sim q\bigg] \to s$

Distribute: . . . . $\bigg[(p \:\vee \sim q) \wedge (q \:\vee \sim q)\bigg] \to s$

. . . . . . . . . . . . . . . $\bigg[(p \:\vee \sim q) \wedge t\bigg] \to s$

. . . . . . . . . . . . . . . . . . $(p \:\vee \sim q) \to s$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

How far should we go? . . . There's no limit . . .

$(p \;\vee \sim q) \to s$

. . $\sim(p \;\vee \sim q) \vee s$

. . . $(\sim p \wedge q) \vee s$ . . . another answer

$(p \:\vee \sim q) \to s$

. . $(\sim q \vee p) \to s$

. . $(q \to p) \to s$ . . . and another

4. thank u very much friends for helping and sharing the solution (ı dont know advenced level english but ı know upper-intermeiated so maybe ı did some mistake writing ıam hoping u can understand. )

5. 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

6. ı could do it