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Discrete Mathematics
1. Write the multisets of prime factors for the given numbers.
I. 160
II. 120
III. 250
2. Write the multiplicities of each element of multisets in part 2(1-I, ii,iii) separately.
3. Find the cardinalities of each multiset in part 2-1.
2. Function converts Fahrenheit temperatures into Celsius. What is the function for opposite conversion?
I. 160
II. 120
III. 250
2. Write the multiplicities of each element of multisets in part 2(1-I, ii,iii) separately.
3. Find the cardinalities of each multiset in part 2-1.
2. Function converts Fahrenheit temperatures into Celsius. What is the function for opposite conversion?
Discrete Mathematics
1. Develop truth tables and its corresponding Boolean equation for the following scenarios.
i. ''If the driver is present AND the driver has NOT buckled up AND the ignition switch is on, then the warning light should turn ON.''
ii. If it rains and you don't open your umbrella, then you will get wet.
i. ''If the driver is present AND the driver has NOT buckled up AND the ignition switch is on, then the warning light should turn ON.''
ii. If it rains and you don't open your umbrella, then you will get wet.
Discrete Mathematics
1. Discuss two real world binary problems in two different fields using applications of Boolean Algebra
Discrete Mathematics
Part 1
1. Describe the characteristics of different binary operations that are performed on the same set.
2. Justify whether the given operations on relevant sets are binary operations or not.
i. Multiplication and Division on se of Natural numbers
ii. Subtraction and Addition on Set of Natural numbers
iii. Exponential operation: on Set of Natural numbers and set of Integers
1. Describe the characteristics of different binary operations that are performed on the same set.
2. Justify whether the given operations on relevant sets are binary operations or not.
i. Multiplication and Division on se of Natural numbers
ii. Subtraction and Addition on Set of Natural numbers
iii. Exponential operation: on Set of Natural numbers and set of Integers
Discrete Mathematics
Justify if the following operations on relevant sets are binary operations or not.
1) Multiplication and Division on se of Natural numbers
2) Subtraction and Addition on Set of Natural numbers
3) Exponential operation: (x,y)→x^y on Set of Natural numbers and set of Integers
1) Multiplication and Division on se of Natural numbers
2) Subtraction and Addition on Set of Natural numbers
3) Exponential operation: (x,y)→x^y on Set of Natural numbers and set of Integers
Discrete Mathematics
Find the simplest form for the following boolean expressions using algebraic methods.
1. (A+B̄)(B+C)+(A+B)(C+Å̄)
2. (A+B)(AC+AC̄)+AB+B
1. (A+B̄)(B+C)+(A+B)(C+Å̄)
2. (A+B)(AC+AC̄)+AB+B
Discrete Mathematics
Produce truth tables for given Boolean expressions.
1) ĀB̅C+AB̅C̄+ABC+ĀBC̄
2) (A+B+C)(A+B+C)(Ā+B+C̄)
1) ĀB̅C+AB̅C̄+ABC+ĀBC̄
2) (A+B+C)(A+B+C)(Ā+B+C̄)
Discrete Mathematics
A company wants to select no more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that no more than 2 will be selected, assuming that the P variables are binary and represent whether a project is selected (value of 1) or not (value of 0)?
Discrete Mathematics
Discuss two real world binary problems in two different fields using applications of Boolean Algebra
Discrete Mathematics
1. Construct a proof for the five color theorem for every planar graph.
