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Discrete Mathematics
Let P(x) is a predicate and the domain of x is the set of all real numbers,let R be “∀x∈Z.P(X),” let S be
“∀x∈Q.P(X),” and let T be “∀x∈R.P(X),”
Find a definition for P(X) (but do not use “ x∈Z “ so that R is true and both S and T are false.
“∀x∈Q.P(X),” and let T be “∀x∈R.P(X),”
Find a definition for P(X) (but do not use “ x∈Z “ so that R is true and both S and T are false.
Discrete Mathematics
The maximum number of perfect matching in a complete bipartite graph Kn,n is
a) n!
b) 2n
c) n2
d) n
a) n!
b) 2n
c) n2
d) n
Discrete Mathematics
Different partially ordered sets may be represented by the same Hasse diagramif they are
a) same
b) lattices with same order
c) isomorphic
d) order-isomorphic
a) same
b) lattices with same order
c) isomorphic
d) order-isomorphic
Discrete Mathematics
explain why a finite automaton does or does not correspond to a graph
Discrete Mathematics
when is a set said to be poset
Discrete Mathematics
prove that 1^2+3^2+5^2+...+(2n+1)^2 = (n+1)(2n+1)(2n+3)/3 whenever n is a nonnegative integer.
Discrete Mathematics
prove that every subdivision of a nonplanar graph is nonplanar
Discrete Mathematics
prove that every subgraph of a planar graph is planar
Discrete Mathematics
The universal set is the set of the integers from 1 to 25, both inclusive. The sets P, Q and R are defined as
P= {p:p is a multiple of 2}
Q= {q:q is a multiple of 3}
R= {r:r is a multiple of 9}
Illustrate the relationship of P, Q and R in a Venn diagram and mark the numbers in each region.
P= {p:p is a multiple of 2}
Q= {q:q is a multiple of 3}
R= {r:r is a multiple of 9}
Illustrate the relationship of P, Q and R in a Venn diagram and mark the numbers in each region.
Discrete Mathematics
Use a truth table to determine whether the argument given below is valid:
If it is a wild animal, it is dangerous. If it is dangerous, it will hurt
you. However, it is not dangerous. Therefore, it is not a wild animal.
If it is a wild animal, it is dangerous. If it is dangerous, it will hurt
you. However, it is not dangerous. Therefore, it is not a wild animal.
