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# Boolean Algebra

### Digital Logic: Boolean Algebra

Write Boolean expression & draw the gate logic diagram & typical PLC logic ladder diagram for a control system wherein a fan is to run only when all of the following conditions are met: - Input A is OFF - Input B is ON or input C is ON, or both B and C are ON - Inputs D and E are both ON - One or more of inputs F, G, or H

### Hasse Diagram: Example Problem

Please see the attached file for the fully formatted problems. Consider the following Hasse Diagram of a partial ordering relation R on a set A. 5 / 3 / 4 | |

### Reflexive, Antisymmetric and Transitive Properties

Please see the attached file for the fully formatted problems. Let A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff m|n. Write the definitions of the properties, reflexive, antisymmetric and transitive and the use the definitions to determine whether each property holds for this relation. (a) Is thi

### Hasse Diagram : Ordered Pairs and Boolean Matrix

Consider the following Hasse diagram of a partial ordering relation R on a set A: (see attached for image) (a) List the ordered pairs that belong to the relation. (b) Find the (boolean) matrix of the relation.

### Application of Set Theoretic Model of Sequences

1. Using the set-theoretic model of sequences, define the following operators, giving their syntax and their semantics: (a) overwrite: given any sequence, s, over a set X, any element, e, of X and any non-zero natural number, n, return a sequence identical to s except that the element at position n is e. For example, overwri

### Writing a linear-time boolean function for a HEAP structure.

Write a linear-time Boolean function HEAP(T:BINARY_TREE) which returns TRUE is T is a heap, i.e., it is partially ordered. Assume that T is represented using pointers to left and right children. Prove that the time is really linear.