# Discrete Structure MCQs

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**________ is a correct definition of a set.**(A collection of unordered elements)**________ symbol is used to represent the “subset” relation between two sets.**(âŠ‚)**________ is true about the empty set (âˆ…).**Â (It is a subset of all sets)**The complement of a set A with respect to a universal set U is denoted by**(A’)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**If A = {1, 2, 3} and B = {3, 4, 5},Â A âˆ© B isÂ**Â Â ({3})__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The power set of a set A isÂ**Â (The set of all subsets of A)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.- _______
**represents the Cartesian product of sets A and B.**Â Â (A Ã— B) **If A and B are disjoint sets, A âˆª B isÂ**( A âˆª B = A âˆ© B )__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â Â**If |A| = 10 and |B| = 5, the maximum possible value of |A âˆ© B| isÂ**Â (5)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.- _____
**operations is associative for sets.Â**Â (Union (âˆª) ) **In graph theory, a graph is defined asÂ**(A set of vertices connected by edges)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The degree of a vertex in a graph is defined asÂ**(The number of edges adjacent to the vertex)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**A complete graph is a graph in whichÂ**Â (Every vertex is connected to every other vertex)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â .__Â**A graph that contains a cycle is calledÂ**Â (A cyclic graph)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The chromatic number of a graph representsÂ**Â (The minimum number of colors needed to color the vertices of the graph such that no adjacent vertices have the same color)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**________ is true about a bipartite graph.**Â (It can be colored with two colors)**The complement of a graph G is a graph thatÂ**(Contains the same number of vertices as G, with all the edges that were in G removed and all the edges that were not in G added)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**A tree is a connected acyclic graph withÂ**(n-1 vertices and n-1 edges, where n is the number of vertices)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â

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**The shortest path between two vertices in a weighted graph is found usingÂ**Â (Dijkstra’s algorithm)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**An Eulerian cycle in a graph is a cycle thatÂ**Â (Visits every edge exactly once and ends at the starting vertex)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**In Boolean algebra, the two possible values are**Â (0 and 1, True and False, On and Off)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â .__**The basic operations in Boolean algebra are**(AND, OR, NOT)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â Â**The complement of a Boolean variable A is denoted as**Â (A’, AÌ…, Â¬A)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The Boolean expression A AND (B OR C) can be simplified using**(Distributive law)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The Boolean expression (A AND B) OR (A AND C) can be simplified to**__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â .__(A OR B) AND (A OR C)**De Morgan’s laws state that the complement of a Boolean expression (A AND B) is equivalent to**Â (A’ AND B’)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**The Boolean expression A XOR A is equal to**Â (A AND A’)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The Boolean expression A NAND B is equivalent to**Â (NOT (A AND B))__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The Boolean expression (A OR B) AND (A OR C) can also be written as**(A AND B) OR (A AND C)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**In graph theory, a tree is defined as a connected graph with**Â (No cycles)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The number of edges in a tree with n vertices is**Â (n – 1)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**A tree with n vertices has exactlyÂ**Â Â (n)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__Â leaves.**The height of a tree is defined as**Â (The number of edges in the longest path from the root to a leaf)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The root of a tree is**Â Â (The topmost vertex in the tree)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**________ is true about a binary tree.**Â Â (Each vertex has at most two children)**A binary tree is considered complete if**(Each level is completely filled except for the last level, which is filled from left to right)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The preorder traversal of a binary tree visits the vertices in the**(Root, Left, Right)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__Â order.**The post order traversal of a binary tree visits the vertices in the________**(Left, Right, Root)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__Â order.

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**The height-balanced property of an AVL tree guarantees that the height of the left and right subtrees of any node differ by at most**(1)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**In propositional logic, a proposition is**Â (A statement that can be either true or false)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The logical operator “AND” is represented by the symbol**Â (âˆ§)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The logical operator “OR” is represented by the symbol**(âˆ¨)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The negation of a proposition p is represented by the symbol**Â (Â¬)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The implication operator in propositional logic is represented by the symbol**Â (â†’)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The logical operator “XOR” stands for**Â (Exclusive Or)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**De Morgan’s laws state that the negation of a conjunction (AND) is equal to**Â (The negation of the first proposition OR the negation of the second proposition)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.**The logical operator “NAND” is represented by the symbol**(â†“)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**The logical operator “NOR” is represented by the symbol**(âˆ¨)__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â__.Â**If x is a prime number belonging to the set of natural numbers (N), then x is an ________ set.Â**Â (Infinite)**Convert the set x, which consists of positive prime numbers that divide 72, into roster form is ________.Â**{2, 3}**The intersection of the sets {1, 2, 8, 9, 10, 5} and {1, 2, 6, 10, 12, 15} is _____________**.Â {1, 2, 10}**If n(P) = 20, n(Q) = 30, and n(P U Q) = 40, then n(P âˆ© Q) is ________.Â**(10)**________ can be considered as discrete objects.Â Â**(Rational numbers, Integers, People)**If the functions g and f are onto functions, then the function (gof) is a _________ function.Â**(onto)**7. If set P consists of 4 elements and set Q consists of 5 elements, then ________ injections can we define from set P to set Q.**Â (120)**________ bytes are needed to encode 2000 bits of data.**Â (2 bytes)**The cardinality of the set of even positive integers less than 20 is ________. (9)****If P = {2, 8, 12, 15, 16} and Q = {8, 16, 15, 18, 9}, then the union of P and Q is ___________.**Â Â {2, 8, 9, 12, 15, 16, 18}**Consider two positive numbers a and b less than one. the maximum values of Ceil(a+b) and Floor(a+b) are ________.Â**Â (Ceil(a+b) is 2 and Floor(a+b) is 1)**The negation of the bits “1001011” is ________.Â**(0110100)**If the bits of Y = 100110 and the bits of X = 001101, the output of X (Ex-or) Y is ________.**Â (101011)**________ Law of Boolean would prove X.X=X.**Â (Idempotent Law)**________ condition is appropriate when adding two matrices.**Â (The columns of both matrices that we want to add are equal)**The Universal logic gate is ________.**Â (NAND)**________ types of canonical forms exist for a Boolean Expression.Â**Â (Two)**In complexity theory, ________ case does NOT exist.**Â (Null Case)**The primary use of Boolean algebra is ________.**Â (To design digital computers)**________ search compares every element against the searching element until it is not found.**Â (Sequential)**In mathematics, a sequence is ________.**Â (An infinite list of numbers in a specific order)**The sum of the terms in a sequence is called a ________.**Â (Series)**The nth term of an arithmetic sequence can be calculated using the formula ________.Â Â**(an = a_{1}+ (n – 1)d)**The sum of the first n terms of an arithmetic series can be calculated using the formula ________.Â**Â (Sn = n(a_{1}+ an)/2)**The nth term of a geometric sequence can be calculated using the formula ________.Â**Â (an = a_{1}* (n – 1)r)**The sum of the first n terms of a geometric series can be calculated using the formula ________.**Â (Sn = a_{1}* (1 – rn)/(1 – r))

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**The sum of the first n natural numbers can be calculated using the formula ________.Â**Â (Sn = n(n + 1)/2)**The sum of the squares of the first n natural numbers can be calculated using the formula ________.Â**(S_{n}= n(n + 1)(2n + 1)/6)**The sum of the cubes of the first n natural numbers can be calculated using the formula________.**Â (S_{n}= n(n – 1)(2n + 1)/6)**The sum of an arithmetic series with a common difference of d, starting from a**Â (S_{1}, and ending at an, can be calculated using the formula ________._{n}= (n/2)(2a_{1}+ (n – 1)d))**The probability of getting a head when flipping a fair coin is ________.**Â (0.5)**If two fair dice are rolled, the probability of getting a sum of 7 is ________.**Â (1/6)**A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random from the bag, the probability of getting a red ball is ________.**Â (5/8)**In a deck of 52 playing cards, the probability of drawing a heart is ________.**(1/4)**A box contains 10 red balls and 5 green balls. If two balls are drawn at random without replacement, the probability that both balls are red ________.**Â (1/15)**If the probability of an event A is 0.3 and the probability of an event B is 0.5,Â the probability of both events A and B occurring is ________.**Â (0.15)**A fair six-sided die is rolled twice.Â The probability of getting a sum of 9 or more is ________.**Â (1/3)**In a group of 20 people, 10 are men and 10 are women. If two people are selected at random, the probability that both are men is ________.**Â (1/4)**For a set of vertices, the ________Â paths from the source are already known.Â**(Shortest)**Cost adjacency matrices represent graphs, where cost represents the edge ________.**(Weight)**The diagonal values of the graph’s cost adjacency matrix are all ________.Â**(Infinite)**If no path exists between vertex Vs and another vertex Vi, then Vs is represented by ________.Â**(+âˆž)**All weights have been assumed ________ in this algorithm.Â**(Positive)**Predicate logic deals with propositions containing ________, which are variables.**Â (Variables)**Predicates represent one or more variables that are determined in a specific ________.**Â (Domain)**A predicate with variables can be made into a proposition by ________.**(Assigning a value to a variable, Quantifying the variable)**A ________quantifies a variable of a predicate.Â**(Quantifier)**Types of quantifiers are there in predicate logic are ________.Â**(2)**The quantifier âˆƒ is called the ________ quantifier.**Â (Existential)**The quantifier âˆ€ is called the ________ quantifier.Â**(Universal)**The rule for the negation of a quantified proposition is ________.**(De Morgan’s law)**Multiple quantifiers can be used to quantify propositions with________****variables.**Â (More than one)

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