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IS143: Discrete Structure

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The big-theta notation for fNo = nlog(n2

+ 1) + n

2logn is?
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Let Q(x, y) be the statement “x + y = x − y.” If

the domain for both variables consists of all integers, what is the truth value

of

xQ(x, 4).

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Let L(x, y) be the statement “x loves y,” where

the domain for both x and y consists of all people in the world. Use

quantifiers to express, “Joy is loved by everyone.”

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Let P(x) denote the statement “x = x + 7.” What

is the truth value of the quantification

xP(x), where the domain consists of all real numbers?

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Determine the truth value of nm(n + m = 5 n − m = 2) if the domain for all variables consists of all integers.
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If f(x) = 3x2 + x3

logx,

then f(x) is?

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The big-O notation for fNo = 2log(n!) + (n2

+ 1)logn is?

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The big-O notation for fNo = (nlogn + n2)(n3

+ 2) is?

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A relation R is defined on the set of integers as aRb if and only if a+b is even and R is termed as ______
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Determine the number of possible relations in an antisymmetric set with 19 elements.
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