Boolean Algebra and Switching Functions

# Boolean Algebra and Switching Functions - Boolean Algebra...

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Boolean Algebra and Switching Functions Set 1, problems 1,5,6 1. Let n ≥ 2. If x is a Boolean variable for all 1 ≤ i n , prove that a) (x + x + ・ ・ ・ + x ) = x x ・ ・ ・ x b) (x x ・ ・ ・ x ) = x + x + ・ ・ ・ + x 5. Let be a Boolean algebra that is partially ordered by≤. If x, y, z , prove that x + y z if and only if x z and y z . 6. State and prove the dual of the result in Exercise 5. Switching Functions: Disjunctive and Conjunctive Normal Forms 1. Find the value of each of the following Boolean expressions if the values of the Boolean variables w , x , y , and z are 1, 1, 0, and 0, respectively. a) xy + x y b) w + xy c) wx + y + yz d) (wx + yz) + wy + (w + y)(x + y)

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2. Let w , x , and y be Boolean variables where the value of x is 1. For each of the following Boolean expressions, determine, if possible, the value of the expression. If you cannot determine the value of the expression, then find the number of assignments
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Boolean Algebra and Switching Functions - Boolean Algebra...

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