A Deduction Problem #1

If Barcelona wins the championship, fans riot. If Barcelona doesn’t win the championship, fans will not go to work. The fans either go to work or cry out of depression. The fans do not riot.
Are the fans crying out of depression?
Solution
1. If Barcelona wins the championship, fans riot.

> Fans do not riot.
> Therefore, Barcelona do not win the championship.

2. If Barcelona does not win the championship, fans do not go to work.

> Barcelona does not win the championship.
> Therefore, fans do not go to work.

3. Fans either go to work or cry out of depression.

> Fans do not go to work.
> Therefore, fans are crying out of depression.

Solution using Symbolic Logic
Barcelona wins = w
Fans riot = r
Fans go to work = g
Fans cry out of depression = c
1. w > r
2. ~ w > ~ g
3. g ∨ c
4. ~ r
5. ~ w (1,4 MT)
6. ~ g (2,5 HS)
7. c (3,6 DS) (Conclusion)
Therefore, fans will cry out of depression.

Source of the problem statement
A fantastic Youtube video playlist called “Logic 101 MOOC” by William Spaniel.
Link> Logic 101 MOOC

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Rules of Inference and Replacement قوانين الإستدلال والإستبدال

Below are the 18 rules of Inference and Replacements that Logicians use for deductions and proofs.
But first we will introduce the symbols of logical operators:
∧ AND (also &)
∨ OR
~ NOT (also ¬)
→ IF..THEN (also >)
⇔ IFF (also equivalence sign ≡)
∀ ALL
∃ SOME

I. The Rules of Inference قوانين الإستدلال

1. Modus Ponens (MP) قياس استثنائي وضعي
p > q
p
Therefore q
2. Modus Tollens (MT) قياس استثنائي رفعي
p > q
~q
∴ ~p

3. Disjunctive Syllogism (DS) قياس منفصل حملي
p V q
~p
∴ q

4. Hypothetical Syllogism (HS) قياس شرطي
p > q
q > r
∴ p > r

5. Constructive Dilemma (CD) 
(p>q)&(r>s)
p∨r
∴ q∨s

6. Conjunction (Conj) إتصال
p
q
∴ p&q

7. Simplification (Simp) تبسيط
p&q
∴ p

8. Addition (Add) إضافة
p
∴ p∨q

II. The Rules of Replacement قوانين الإستبدال

9. Demorgan’s Law (DM) قانون ديمورغن
~(p&q)  (~p∨~q)
~(p∨q)  (~p&~q)

10. Commutivity (Com) تبادل
q∨p  p∨q
q&p  p&q

11. Associotivity (Assoc) تجميع
p∨(q∨r)  (p∨q)∨r
p&(q&r)  (p&q)&r

12. Distribution (Dist) توزيع
p∨(q&r)  (p∨q)&(p∨r)
p&(q∨r)  (p&q)∨(p&r)

13. Double Negation (DN) نفي مزدوج
~~q  q

14. Transportation (Trans) نقل
p>q  ~q>~p

15. Material Implication (Impl)
p>q  ~p∨q

16. Material Equivalence (Equiv)
p≡q  (p>q)&(q>p)

17. Exportation (Exp) تصدير
p>(q>r)  p>(q&r)

18. Tautology (Taut)
p∨p  p
p&p  p

Source:
A brilliant YouTube video series called “100 Days of Logic” by Carneades.org
Link > 100 Days of Logic
In addition to my friend λόγος, who is a great Thinker and Logician.

What can P and J tell you about the MBTI type cognitive functions

The P or J letters tells you the type of the first extraverted function.

For example, when you pick the ENTP, the P tells you that the first extraverted function is a perceiving function Pe. So we pick from (NT) the function that is perceiving, which is N. And it is extraverted, therefore Ne.

Now since ENTPs are extroverts, Ne is the first function. Followed by T which will be Ti. Then Fe (not Se, as S has to be a polar opposite of a perceiving function, in this case Ne, so S must be Si, and therefore is the fourth or the inferior function). Also F has to be the polar opposite of the other judging function T. and since T is introverted (Ti) and is the second or auxiliary function; F must be an extroverted function; therefore Fe. As a result, the function stack of the ENTP will become: Ne Ti Fe Si.

Similarly, for INFJs. J implies that their first extroverted function is a judging function Je. So from NF we pick F, and it’s extroverted, so Fe. But the INFJ is introverted, which means that its dominant function must be introverted. As a result, we deduce that of the two major functions of INFJ, which are N and F; the dominant and introverted function is Ni. The polar opposite of the dominant function is Se, and it must be the last function. Similarly, the polar opposite of the auxiliary function Fe is Ti, and it is the third function. Therefore, the function stack of the INFJs will be: Ni Fe Ti Se.