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Prove that, the complement of each element in a Boolean algebra B is unique.
Ans: Proof: Let I and 0 are the unit and zero elements of B correspondingly. Suppose b and c be two complements of an element a ∈ B. After that from the definition, we have
a ∧ b = 0 = a ∧ c and
a ∨ b = I = a ∨ c
We can write b = b ∨ 0 = b ∨ (a ∧ c )
= (b ∨ a) ∧ (b ∨ c) [as lattice is distributive ]
= I ∧ (b ∨ c )
= (b ∨ c )
Likewise, c = c ∨ 0 = c ∨ (a ∧ b )
= (c ∨ a) ∧ (c ∨ b) [as lattice is distributive]
= I ∧ (b ∨ c) [as ∨ is a commutative operation]
= (b ∨ c)
The above two results define that b = c.
Larry earned $32,000 per year. Then he received a (3)1/4% rise. What is Larry's salary after the raise? If Larry earns a (3) 1/4 % (or 3.25%) raise, he will earn 103.25% of his
how to solve addition
In a parallelogram ABCD AB=20cm and AD=12cm.The bisector of angle A meets DC at E and BC produced at F.Find the length of CF.
40.783-75
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
Evaluate the given limits, showing all working: Using first principles (i.e. the method used in Example 1, Washington 2009, Using definition to find derivative ) find the
2 of 10 =
Need a problem solved
Q. What is Addition Rule of probability? Ans. Suppose there are 17 girls and 15 boys in your stats class. There are 17 + 15 = 32 ways for your teacher to pick one student
what is 8e^3x + 4 = 15
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