Question 4. The following are logical laws shown in our lecture. Find their dual versions if exist. Implication law Idempotent lauw Commutative law A → B = ¬AV B ΑΛΑ Α АЛВ 3D ВЛА (АЛ В) ЛС %3 АЛ (ВЛС) АЛ (AV B) А Associative law Absorption law АЛ (BVC) (АЛ В)V (AЛС) Distributive law Double Negation law De Morgan's law Excluded middle law ¬A = A ¬(A ^ B) = ¬AV¬B A^¬A = F Identity law Domination law AAT = A ΑΛF F

3

Please don't ptovide handwritten solution .....

Let x, y, z ∈ { 0, 1 } be bits, and let ϕ be the logical expression ϕ(x,y,z) = (x ⇒ y) AND ((y AND z) ⇒ x). for which combinations of ϕ(x,y,z) is ϕ true(i.e 1)? Example: ϕ(1,1,1) is a combination of ϕ(x,y,z)

Which postulate justifies that ДНАМ-ДСОW? H. а. АА C. ASA b. SSA d. SAS

Which among the following statements is (are) true? * VXvy,M(x,y)=vyvx,M(x,y) O vxay,M(x,y)=ayvx,M(x,y) All of these ООО

Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?(i) {3, 4} ⊂ A                                             (ii) {3, 4} ∈ A                                            (iii) {{3, 4}} ⊂ A(iv) 1 ∈ A                                                   (v) 1 ⊂ A                                                  (vi) {1, 2, 5} ⊂ A(vii) {1, 2, 5} ∈ A                                   (viii) {1, 2, 3} ⊂ A

Argument 5: Premise: Premise: Conclusion: Argument Form? Argument 6: Premise: (C 5 J) • (~P = W) Premise: Cv mP Conclusion: ~) v W Argument Form? Argument 7: Premise: Premise: Conclusion: Argument Form? Argument 8: Premise: Premise: Conclusion: Arqument Form?

16. The statement: (e h) = (g h) is logically equivalent to O -[(-e v h) A (e v ~h)] A [(~g v h) A (g v ~h)] O (-e v h) A (e v ~h)] v [(~g v h) A (g v ~h)] O [(-ev h) A (e v ~h)] ^ [[~g v h) ^ (g v ~h)] O [(-ev h) A (ev ~h}] v [(~g v h) A (g v ~h)] O(-evh) A (e v h]] v [(-g vh) A (g v ~h)] O none