Discrete Mathematics

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?

Let P(x) be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used ar...

A = {0, 1, 2, 3, ...} is the set of non-negative integers. Let F be the set of functions from A to itself. For any two functions, f1, f2 ∈ F, we define (f1⨀f2)(n) = f1(n) + f2(n) f...

Let P be the partial order defined on the set {1,2,3,4} as follows P = {(x,x) | x ∈ {1,2,3,4}} ∪ {(1,2), (3,2), (3,4)} The number of total orders on {1,2,3,4} that contain P is ___...

Consider the operators ◊ and □ defined by a◊ b = a + 2b, a□b = ab, for positive integers. Which of the following statements is/are TRUE?

Let p, q, r denote the statements "It is raining", "It is cold", and "It is pleasant", respectively. Then the statement "It is not raining and it is pleasant, and it is not pleasan...

Consider the set $X = \{a,b,c,d,e\}$ under the partial ordering $R = \{(a,a), (a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e), (c,c), (c,e),(d,d),(d,e),(e,e)\}$. The Hasse diagram of the...

Suppose p is the number of cars per minute passing through a certain road junction between 5PM and 6PM and p has a poisson distribution with mean 3. What is the probability of obse...

Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

Let $$a(x,y)$$, $$b(x,y)$$ and $$c(x,y)$$ be three statements with variables $$x$$ and $$y$$ chosen from some universe. Consider the following statement: $$$\left( {\exists x} \rig...

What is the number of vertices in an undirected connected graph with $$27$$ edges, $$6$$ vertices of degree $$2$$, $$\,\,$$ $$3$$ vertices of degree 4 and remaining of degree 3?

The recurrence equation $$\,\,\,\,\,\,\,T\left( 1 \right) = 1$$ $$\,\,\,\,\,\,T\left( n \right) = 2T\left( {n - 1} \right) + n,\,n \ge 2$$ evaluates to

Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$, the va...

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?

Solve the following recurrence relation $$\,\,\,\,\,\,\,{x_n} = 2{x_{n - 1}} - 1\,\,n > 1$$ $$\,\,\,\,\,\,\,{x_1} = 2$$