DISCRETE MATH EXAMINATION QUESTIONS WITH COMPLETE SOLUTIONS GRADED A+
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DISCRETE MATH
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DISCRETE MATH
DISCRETE MATH EXAMINATION QUESTIONS WITH COMPLETE SOLUTIONS GRADED A+
what is predicate? - Answer-The predicate tells what the subject is or does. the domain is? - Answer-all values that can be substituted to predicate
P(x) => Q(x) - Answer-every element in truth set of P is in the truth set ...
DISCRETE MATH EXAMINATION
QUESTIONS WITH COMPLETE
SOLUTIONS GRADED A+
what is predicate? - Answer-The predicate tells what the subject is or does.
the domain is? - Answer-all values that can be substituted to predicate
P(x) => Q(x) - Answer-every element in truth set of P is in the truth set of Q
P(x) <=> Q(x) - Answer-truth sets are identical
Negation of Quantifiers - Answer-quantifier and predicate negates
A is subset of B - Answer-A ⊆ B, every element in A is in B
Proper subset - Answer-If A ⊆ B, and There is at least one element in B that is not in A
Proofing the subset relation - Answer-Take an arbitrary element in subset
Set Equality - Answer-A and B equals, A=B, if every element of A is in B, abd B in A
A ⊆ B and B ⊆ A
Set Union - Answer-A U B, is the result set that contains elements that at least in one
sets
set intersection - Answer-A ∩ B, elements that are both in A and B
Set difference - Answer-A - B, is the set of elements in A that not in B
Set compliment - Answer-A^c, all elementa outside of A
Disjointed sets - Answer-if set A and B have no common elements
mutually disjoint - Answer-All collection of sets have no common elements
Partition of set A of collection of sets - Answer-A is union of all Ai, and sets are mutually
disjointed
Power set - Answer-Power set of A, is a set of all subsets of A and empty set
, Cartesian product of sets ordered - Answer-A x B, take one element in A, and make
combination with every element in B, then go to next element in A
A ∩ B ⊆ A - Answer-union, intersection and difference first, then inclusionA
⊆ A 𝖴 B - Answer-inclusion
transitivity of sets - Answer-A ⊆ B and B ⊆ C, then A⊆C
compliment law - Answer-(A^c)^c = A
de Morgan for sets - Answer-(A 𝖴 B)^c = A^c ∩ B^c
Set difference law - Answer-A - B = A ∩ B^c
f: X -> Y - Answer-X domain, Y codomain, there is only single arrow from X to Y. But to
the element in Y, can go two separate arrows
identity function - Answer-Ix = x. each element maps to itself
inverse image of function - Answer-F(1) = 4, F^(-1)(4) = 1
one-to-one function - Answer-if F(x1) = F(x2), then x1 = x2. Arrow points from element X
to only one element Y. Every element in X should map to Y. can be free elements in Y
Onto functions - Answer-given element in Y, it's possible to find an element that maps to
Y. Every element in Y should have element/s in X that maps to it.
bijection - Answer-if both one-to-one and onto
composition function - Answer-(g ° f)(x) = g(f(x))
composition and inverse - Answer-f ° f^-1 = Ix
Composition one-to-one/onto - Answer-then relation is one-to-one/onto
what is a statement? - Answer-is a sentence that is true or false but not both
p but q - Answer-p and q
negation - Answer-~p (not p)
conjunction - Answer-p 𝖠 q
disjunction - Answer-p ∨ q
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