Discrete Mathematics Answers

Let Kn be such that vertices are labeled 1,2,3....n. number of simple paths between v1 and vn such that the labels on the paths are strictly increasing
a) 2^n
b) 2^n-2
c) (n-2)!
d) n!

identity , equal , equivalent --- are used in mathematics . are identity and equal both same ?? if same then we can put = sign in every identity . but Identities are sometimes indicated by the triple bar symbol ≡ instead of = ------ what does it mean?? if we use the triple bar ≡ , then it becomes equivalent .now we can say identities are sometimes equivalent. is it true? it becomes confusing .please explain with example . please help to learn the actual concept.

(a) If A and B given below are two sub-sets of universal sets of natural number ranging from 2 to 16.
A = {6,7,8,9,10,11,12,13,15}
B = {2,4,6,8,10,12,14}
Find:
Complement of A i.e AC
A complement union B complement i.e AC∪ BC

For each of the following words: if it is a sentence in the grammar, draw its derivation
tree; if it is not a sentence, explain carefully how you know that it is not a sentence.

(i) a/b − c/d ∗ e + f

A relation R defined on a set S is said to be ………… if b R a
∀a,b∈S
.
a. transitive
b. reflexive
c. symmetric
d. none of the above

A rule which associates every element of a non-empty set A exactly on element of a non-empty set B is called a ……….

a. equation
b. function
c. subset
d. set

The largest set containing all elements under consideration is known as ……. set.
a. universal
b. university
c. unity
d. unicorn

…………… is the set of integers

a. {0, ±1, ± 2, ± 3…… }
b. {0,1, 2, 3, ……}
c. {±1, ± 2, ± 3…… }
d. {1, 2, 3, ……}

…………… is the set of natural numbers

a. {1, 2, 3, ……}
b. {0,1, 2, 3, ……}
c. {±1, ± 2, ± 3 …… }
d. {0, ±1, ± 2, ± 3 …… }

Given that S = { a, b, c, d , e } and T = { a, c, e }, then one of these is untrue

a. T is a subset of S

b. T⊆S

c. S≠T

d. S⊆T