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Discrete Mathematics – Q&A


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write the following boolean expressions in an equivalent sum of product canonical form in three variables x1, x2, and x3:
1. x1*x2 ?
2. x1⊕x2 ?
3. (x1⊗X2)'*X3
Simplify the following Boolean function using k -map
F = A’C + A’B + AB’C + BC
Expand the following Boolean functions into their canonical form:
i. f(X,Y,Z)=XY+YZ+X'Z+X'Y'
ii. f(X,Y,Z)=XY+X'Y'+X'YZ
Expand the following Boolean functions into their canonical form:
i. f(X,Y,Z)=XY+YZ+ X Z+ X Y
ii. f(X,Y,Z)=XY+ X Y + X YZ
If we have 100 people (80 male and 20 female) and we need to choose a committee.
The committee must contain exactly 2 females, then how many different 5 person committees are possible?
In a certain village of 1000 houses, 750 have a car, 800 have a refrigerator, 850 have a telephone and 950 have a radio. What is the least number of houses that have all four?
How many bit strings of length five either begin or end with a 1?
How many maximum number of bit strings of length five are possible?
Roxanne sits and writes roxyroxyroxyroxyroxy... If she continues, determine the 2134th letter she will write down
write the following sentence in predicate calculus.
Every teacher takes care of his student.john is the teacher and James is his student.
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