Discrete Mathematics Definitions - Exam 1 (copy)

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17 Terms

1

If a and b are integers, a divides b

if there exists an integer k so that b = ak

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2

For a natural number n, n! =

n(n−1)(n−2)···3·2·1.

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3

An integer n is even

if there exists an integer k so that it can be written as n = 2k

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4

Two statements are equivalent

if their truth table match for all possible values of the component statements

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5

Let a and b be integers. The greatest common divisor of a and b is denoted by gcd(a,b) and is the natural number d that satisfies the following two conditions

d divides both a and b. If n is an integer that divides both a and b then n divides d.

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6

natural number definition

a counting number as in 1, 2, 3

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7

whole number definition

a counting number or zero as in 0, 1, 2, 3

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8

integer definition

a positive or negative counting number or zero

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9

An integer n is odd

if there exists an integer k so that it can be written as n = 2k +1

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10

mathematical statement definition

a declarative sentence which is either true or false.

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11

negation definition

a statement having the opposite truth value of the original statement.

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12

A conditional statement is

one of the form If P then Q

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13

The converse of the conditional statement "If P, then Q" is

If Q, then P

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14

The inverse of the conditional statement "If P, then Q" is

If not P, then not Q

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15

The contrapositive of the conditional statement "If P, then Q" is

If not Q, then not P

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16

A number n is a rational number if

it can be written as p/q for some integers p and q where q does not equal 0.

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17

A natural number n is prime if

it has exactly two divisors namely 1 and itself

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