Logical laws theory and solved exercises Laws of propositional algebra Logical laws

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#profeguille Definition of logical laws. 12 logical laws with their corresponding examples LOGICAL LAWS - LAWS OF PROPOSITIONAL ALGEBRA - 12 LAWS Super easy - Mathematics profeguille Video content with examples for each logical law: 00:00 Introduction 00:16 What are the logical laws? 04:05 Law of involution or double negation 05:03 Laws of idempotence 06:24 Laws of the excluded middle 08:26 Commutative laws 10:24 Associative laws 14:38 Distributive laws 17:52 De Morgan's laws 21:00 Conditional laws 23:49 Biconditional laws 27:12 Absorption laws 32:46 Logical laws for exclusive disjunction 35:20 Additional logical laws 37:20 Farewell COMPLETE LOGICAL PROPOSITIONS - PODCAST: ▶️ https://acortar.link/Fq1qGU ✏️ PROPOSITIONAL LOGIC BLOG: https://logicaproposicionalprofeguill... _________________________________________________________________ ProfeGuille Official Website: https://profeguilleq.blogspot.com/ YouTube: / @profeguillematematica Facebook: / quidimat Twitter: / quidimat Instagram: / quidimat Tik Tok: / quidimat _________________________________________________________________ Guillermo Quiñones Diaz, #profeguille Logical laws They are logical equivalences that allow us to simplify a proposition and express it in a simpler way. 1) Laws of involution or double negation: 04:05 Denying a proposition twice is equivalent to affirming the same proposition. ~ (~ p) ≡ p 2) Laws of idempotence: 05:02 It means equal value; this means that, when operating the same proposition with the connectives of inclusive conjunction or disjunction, it is equivalent to the same proposition. a) p ᴧ p ≡ p b) p ᴠ p ≡ p 3) Laws of excluded middle: 06:22 It means that, when operating a proposition with its opposite, the result is false with the conjunction and true with the inclusive disjunction. a) p ᴧ ~ p ≡ F b) p ᴠ ~ p ≡ V 4) Commutative laws: 08:25 To commute means to change place or order. a) p ᴧ q ≡ q ᴧ p b) p ᴠ q ≡ q ᴠ p c) p ↔ q ≡ q ↔ p 5) Associative laws: 10:23 To associate means to group in a different way. a) p ᴧ q ᴧ r ≡ ( p ᴧ q ) ᴧ r ≡ p ᴧ ( q ᴧ r ) b) p ᴠ q ᴠ r ≡ ( p ᴠ q ) ᴠ r ≡ p ᴠ ( q ᴠ r ) c) p ↔ ( q ↔ r ) ≡ (p ↔ q) ↔ r 6) Distributive laws: 14:38 a) p ᴧ (q ᴠ r) ≡ (p ᴧ q) ᴠ (p ᴧ r) b) p ᴠ (q ᴧ r) ≡ (p ᴠ q) ᴧ (p ᴠ r) c) p → ( q ᴧ r ) ≡ ( p → q ) ᴧ ( p → r ) d) p → ( q ᴠ r ) ≡ ( p → q ) ᴠ ( p → r ) 7) De Morgan's Laws: 17:52 By denying a conjunction or disjunction of two propositions we will obtain the negation of each of these, but changing the conjunction for the disjunction and vice versa. a) ~ ( p ᴧ q ) ≡ ~ p ᴠ ~ q b) ~ ( p ᴠ q ) ≡ ~ p ᴧ ~ q 8) Conditional laws: 21:00 a) p → q ≡ ~ p ᴠ q b) ~ ( p → q ) ≡ p ᴧ ~ q 9) Biconditional laws: 23:48 a) p ↔ q ≡ (p → q) ᴧ (q → p) b) p ↔ q ≡ (p ᴧ q) ᴠ (~ p ᴧ ~ q) 10) Absorption laws: 27:11 TOTAL ABSORPTION a) p ᴧ (p ᴠ q) ≡ p b) p ᴠ (p ᴧ q) ≡ p PARTIAL ABSORPTION c) p ᴧ (~ p ᴠ q) ≡ p ᴧ q d) p ᴠ (~ p ᴧ q) ≡ p ᴠ q 11) Logical laws for exclusive disjunction: 32:45 a) p ∆ q ≡ ( p ᴧ ~ q ) ᴠ ( q ~ p ) b) p ∆ q ≡ ( p ᴠ q ) ᴧ ~ ( p ᴧ q ) 12) Additional logical laws: 35:19 a) p ᴧ F ≡ F b) p ᴧ V ≡ p c) p ᴠ F ≡ p d) p ᴠ V ≡ V e) V ᴠ V ≡ V f) F ᴠ F ≡ F Super easy - Mathematics profeguille

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