Communications in Algebra, volume 26, number 6, 1998 by Marcel Dekker, Inc

By Marcel Dekker, Inc

Goals and Scope. This magazine provides full-length articles thai replicate major advances in all components of present algebraic curiosity and task.

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35. 36. 37. 35, show that it corresponds to the boolean expression (A ∧ D) ∨ (B ∧ E) ∨ (A ∧ C ∧ E) ∨ (B ∧ C ∧ D). 38. 36 and simplify your circuit. 39. A hall light is controlled by two switches, one upstairs and one downstairs. Design a circuit so that the light can be switched on or off from the upstairs or the downstairs. 40. A large room has three separate entrances, and there is a light switch by each entrance. Design a circuit that will allow the lights to be turned on or off by throwing any one switch.

36, find their disjunctive normal forms, and then try to simplify the circuits. 32. 33. 34. 35. 36. 37. 35, show that it corresponds to the boolean expression (A ∧ D) ∨ (B ∧ E) ∨ (A ∧ C ∧ E) ∨ (B ∧ C ∧ D). 38. 36 and simplify your circuit. 39. A hall light is controlled by two switches, one upstairs and one downstairs. Design a circuit so that the light can be switched on or off from the upstairs or the downstairs. 40. A large room has three separate entrances, and there is a light switch by each entrance.

C, then A C. (reflexivity) (antisymmetry) (transitivity) Proof (i) A ∧ A = A is an idempotent law. (ii) If A ∧ B = A and B ∧ A = B, then A = A ∧ B = B ∧ A = B. (iii) If A ∧ B = A and B ∧ C = B, then A ∧ C = (A ∧ B) ∧ C = A ∧ (B ∧ C) = A ∧ B = A. 9. 17 is called a partial order relation, and a set with a partial order on it is called a partially ordered set or poset for short. 9. A partial order on a finite set K can be displayed conveniently in a poset diagram in which the elements of K are represented by small circles.

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