Discrete Mathematics Answers

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
A = {x / x is an odd number between 5 and 21} is same as------------ (a) A = {5,7,9,11,13,15,17,19} (b) A = {5,7,9,11,13,15,17,19,21} (c) A = {x : x is an odd number between 5 and 21} (d) A = {7,9,11,13,15,17,19,21}

Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once.

Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and
B. Is this data correct? Explain.

Out of 500 students investigated, 400 studies Hindi, 200 English and 50 both. Is this data correct.
Explain and justify your answer.

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