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MTH 2000-1-8
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Terms in this set (19)
Assertion
is a sentence that is either true or false
deduction
a series of hypotheses that is followed by a conclusion
valid
if its conclusion is true whenever all of its hypotheses
are true. In other words, it is impossible to have a situation in which all of the hypotheses are
true, but the conclusion is false.
tautology
if it is true in all situations
contradiction
if it is false in all situations
The set with no elements can be denoted
{ }.∅
subset
We say that B is a subset of A iff every element of B is an element of A
proper subset
we say B is a proper subset of A iff B ⊂ A
and B not= A
union
A ∪ B = { x | x ∈ A or x ∈ B }.
intersection
A ∩ B = { x | x ∈ A and x ∈ B }
set difference
{ x | (x ∈ A) & (x /∈ B) }.
complement
B = U r B = { x | x /∈ B }
disjoint
iff their intersection is empty
(that is, A ∩ B = ∅)
A and B are disjoint ⇔
there does not exist an x, such that
(x ∈ A) & (x ∈ B)
power set
A is the set of all subsets of A.
P(A) = { B | B ⊂ A }
divisor
We say a is a divisor of b (and write "a | b") iff there
exists k ∈ Z, such that ak = b
even
An integer n is even iff 2 | n
odd
An integer n is odd iff 2 not | n
a is congruent to b modulo
a is congruent to b modulo n iff a − b is
divisible by n.
a ≡ b (mod n)
remainder
the number r is called the remainder
when a is divided by n
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