c) Does the equality |A U B| = |A| + |B| hold for some sets A and B? d) Is the composition of two one-one functions a one-to-one function? e) Is it true that P(A) C A?

Q: d) K, has an Eulerian circuit for every natural number n 2 3. e) Every finite poset has a minimal…

A: d)

Q: 4. Show that (N,|) is a poset

A:

Q: 10. Draw the graphs a) K7 b) K18 c) C7

A: The objective is to draw the graph of K7 ,K1,8,C7

Q: f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric? g) Is…

A: Use the definition of antisymmetric to check whether the given relation is antisymmetric or not.…

Q: 1. let the universe be all the positive integers (N). Determine whether the following are true or…

A:

Q: How many permutations of the letters OPQRSTU contain the strings QPO and PRS?

A: Solution

Q: Find the SPI form of the Boolean expression whose Karnaugh map is below. yz _yz yZ ỹz 1 1 | 1 1 wx…

A: From the given table, the input value of Karnaugh map is…

Q: How many bit strings contain exactly eight Os and 10 Is if every 0 must be immediately followed by a…

A: Solution

Q: 5. If A is a set with 5 elements, how many elements are in P(A), the power set of A.

A: The given problem is to find that how many elements are there in power set of A, P(A) Given A is the…

Q: Prove the statement: Let A be a subset of a nonempty finite set U. If P(A)=a, then P(Ā)=1-a.

A: We have to prove given statement...

Q: 10. Two sets are called disjoint if they have no elements in common, i.e., if their intersection is…

A: Note that two sets are called disjoint if they have no elements in common, that is, if their…

Q: There are 20 different time periods during which classes at a university can be scheduled. If there…

A: Solution

Q: 5. Does the graph bellow have a Hamiltonian path? Hamiltonian circuit? If

A:

Q: Select the solution to each of these recurrence relations: 2(n + 1)! 3n + 1 5. (-1)^n 3· (2^n)n! an…

A:

Q: Let f :A→B and g : B +C be functions. Show that if g o f is onto, then g is onto.

A: Given: f:A→B and g:B→C are functions Given: gof: A→C is onto To show: g:B→C is onto That is,  for…

Q: If every telephone in the world is assigned a number that contains a country code 1 to 3 digits…

A: The telephone number has a country code first, followed by 12 digit telephone number of the form…

Q: (a) Suppose f and g are functions whose domains are subsets of Z*, the set of positive integers.…

A: (a) Definition of Big O notation: If f(x)=O(g(x)), then, the absolute value of function f(x)is at…

Q: Base Вачe 2 11100010100.01101 01111111001.1I110

A:

Q: 26. Let E be the set of all even integers, and let O be the set of all odd integers. Let X = {n €Z|n…

A: If y is an even integer then it will be of type 2n for some n in integer If y is an odd integer then…

Q: Assume that the population of the world in 2010 was 6.9 billion and is growing at the rate of 1.1% a…

A: Solutions

Q: 1:if z 1 then z is even " is false, we need to find z such that

A: Given statement is

Q: If there are 1022 different classes at a university, how many different rooms are required in order…

A: according to question, 1022 different classes are there at a university and we have to schedule all…

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A:

Q: 7. An undirected graph is called complete if every vertex shares and edge with every other vertex.…

A: Given: Prove how many edges does the complete graph have with n vertices.

Q: 4. How many different bracelets you can make out of 16 different beads (number different circular…

A: We have to find no difference circular arrangements..

Q: 2. Sometimes light fixtures are controlled by more than one switch. Circuits need to be designed so…

A: Given that the circuit for a light fixture controlled by more than one switch (take 3 switches),…

Q: 29. Sociologists use graphs to model social relationships. A social network (not to be confused with…

A: A social network is a graph where the nodes represent ‘actors’ and the edges represent relationships…

Q: 7. Use set identities or different proof method to show that: (AUBY NA = Ø

A:

Q: 6. Prove or disprove the statements: (a) The function f: Z × Z → Z defined by f(m,n) = m + n +1 is…

A:

Q: 1. Consider the following relations on the set A = {1,2, 3, 4, 5} . (a) R1 = {(1, 1), (1, 2), (3, 3)…

A: (a) Given: A={1, 2, 3, 4, 5}, and the relation defined on A is: R1=1,1,1,2,3,3,3,2 (i) to check if…

Q: 3. (Explicit formula of a recursive sequence) We define a sequence by ao = 7 an = an-1+ 2n - 5 for n…

A: Given recurrence relation is an=an-1+2n-5, n≥1, and a0=7. Characteristic equation: The given…

Q: Show that in a group of people there must be two individuals that have the same number of friends…

A: We make a proof by contradiction and use the pigeonhole principle.

Q: A ternary tree is a tree where every parent node has (at most) three child nodes. For example, the…

A: Given that, A ternary tree is a tree where every parent node has (at most) three child nodes. The…

Q: 30. (i) Verify that Hall's marriage condition is satisfied for the family {A₁, A₂, A3, A4, A5, A6}…

A: Hall's marriage condition is defined as  let S be the family of finite subsets of X, where the…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.