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$$XX = \left\{ {2,3,6,12,24} \right\}$$. 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\}.