We have also provided number of questions asked since 2007 and average weightage for each subject. Provide short answers to the following questions: How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? How many distinct pairs of sequences, $B$ and $C$ are there such that each is sorted in ascending order, $B$ has $5$ and $C$ has $3$ elements, and the result of merging $B$ and $C$ gives $A$ $2$ $30$ $56$ $256$, Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. (a) The union of two equivalence relations is also an equival... (a) How many binary relations are there on a set A with n elements? The number of functions from an $$m$$ element set to an $$n$$ element set is, The number of equivalence relations on the set $$\left\{ {1,2,3,4} \right\}$$ is. This is not the official website of GATE. If it ... go to the shopping mall. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{-1}$ Which of the above is/are equivalence relation/relations? The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. Q. Combinatorics. Consider the following 4 partitions $$\,{\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}$$ o... Let f: $$\,B \to \,C$$ and g: $$\,A \to \,B$$ be two functions and let h = fog. $1638$ $2100$ $2640$ None of the above, The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n-1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above, How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$? Made Easy Test Series:Discrete Math-Mathematical Logic Consider the following first order logic statement I)∀x∀yP(x, y) II)∀x∃yP(x, y) III)∃x∃yP(x, y) III)∃x∀yP(x, y) Which one... true, then III), IV) is true B) If IV) is true, then II), III) is true C) None of these However, a wife need not be accompanied by her husband. ExamSIDE.Com. }{2^n}\) \(^{2n}\mathrm{C}_n\), Let $A$ be a sequence of $8$ distinct integers sorted in ascending order. Some group (G, o) is known to be abelian. If Kareena and Parineeti do not go to the shopping mall then it is raining. $n$ $n+1$ $2^{n-1} + 1$ $n!$, NIELIT SCIENTIST B Technical Assistant ANSWER KEY RELEASED. How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? If a relation R is both symmetric and transitive, then R is reflexive. Thank you ! Then the largest possible size of a subgroup of G other than G itself is ______. Let $G$ be an arbitrary group. Also please explain , as no element has compliment greater than 1 , it may or may not be distributive then is there any feasible way to differentiate between option a and d ? Y, Z$$ be sets of sizes $$x, y$$ and $$z$$ respectively. ACE Academy test series … answered 4 hours ago in Graph Theory by Sherrinford03 (73 points) | 12 views. Linear Algebra. Then. Let C be a collection of distinct subsets of A such that for any two subsets $${S_1}$$ a... Let R and S be any two equivalence relations on a non-emply set A. $4$ $6$ $7$ $9$, The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$. Both $P$ and $Q$ are false. The number of binary relations on a set with $$n$$ elements is: Suppose $$A$$ is a finite set with $$n$$ elements. GATE . Given that h is an onto function which o... Let A be a set with n elements. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, fraction $b$ prefer Birendra to Chanchal and fraction $c$ ... $(a, b, c) = (0.49, 0.49, 0.49);$ None of the above. $Q:$ $R$ is transitive. Consider the following sets. Let f: $$R\,x\,R \to \,R\,x\,R\,$$ be a bijective function defined by f (x, y ) = ... Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Given statement is : ¬ ∃ x ( ∀y(α) ∧ ∀z(β) ) where ¬ is a negation operator, ∃ is Existential Quantifier with the meaning of "there Exists", and ∀ is a Universal Quantifier with the meaning " for all ", and α, β can be treated as predicates.here we can apply some of the standard results of Propositional and 1st order logic on the given statement, which are as follows : [ Result 1: ¬(∀x P(x)) <=> ∃ x¬P(x), i.e. Which one of the following is a closed form expression for the generating function of the sequence $\style{font-family:'Times New Roman'}{\left\{a_n\right\}\;,}$ where $\style{font-family:'Times New Roman'}{a_n=2n+3}$ for all $\style{font-family:'Times New Roman'}{n=0,1,2,.....?} R1: ∀a,b ∈ G, aR1b if and only if ∃g ∈ G such that... Let U = {1, 2 ,..., n}. ... Let $$A$$ be a set of $$n\left( { > 0} \right)$$ elements. negation of "for … $$\left( {P \cap Q \cap R} \right) \cup \left( {{P^c} \cap ... Let $$S$$ be a set6 of $$n$$ elements. ... A partial order P is defined on the set of natural numbers as following. (a) Mr. X claims the following: Similarly a line $L$ in a circuit is said to have a $stuck-at-1$ fault if the line permanently has a logic value $1$. Which one of the following statements is TRUE? Consider the following statements: Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. The set ... Let $$X$$ $$X = \left\{ {2,3,6,12,24} \right\}$$. Let P(S) denote the power set of a set S. Which of the following is always true? Consider the set S = {a, b, c, d}. Given a set of elements N = {1, 2, ....., n} and two arbitrary subsets $$A\, \subseteq \,N\,$$ and $$B\, \subseteq \,N\,... Let S = {1, 2, 3,....., m} , m > 3. Both $P$ and $Q$ are true. Let $$X,. No bridge $\{d,e\}$ $\{c,d\}$ $\{c,d\}$ and $\{c,f\}$, Mala has the colouring book in which each English letter is drawn two times. II. The following is the incomplete operation table of a 4-element group. Then. How many different non-isomorphic Abelian groups of order 4 are there? Let $${X_1},\,....,\,{X_n}$$ be subsets of S each of size 3. 4.7 (26) Here you can download the free lecture Notes of Discrete Mathematics Pdf Notes – DM notes pdf materials with multiple file links to … ∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z =... Let N be the set of natural numbers. education, JNTU World, Notes 9,834 Views. It is our sincere effort to help you. The number of way a person roundtrip by bus from $A$ to $C$ by way of $B$ will be $12$ $7$ $144$ $264$, NIELIT 2017 July Scientist B (CS) - Section B: 11, Consider the following graph $L$ and find the bridges,if any. $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ $((p \wedge q) \vee (\neg p \wedge \neg q))$ and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$, How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? Herw x/y denotes integer division. Please tell any generalized solution for this problem, if exists. The set $$\left\{ {1,\,\,2,\,\,3,\,\,5,\,\,7,\,\,8,\,\,9} \right\}$$ under multiplication modulo 10 is not a group. $ Let $ A=\{(x,\;X)\;\vert x\in X,\;X\subseteq U\}. Let $A$ be a set with $n$ elements. Both prints of a letter can also be coloured with the same colour. A line $L$ in a circuit is said to have a $stuck-at-0$ fault if the line permanently has a logic value $0$. Let $ U=\{1,2,\;...\;,\;n\}.