Let P(x) be the statement "x likes subject mathematics," where the domain for x consists …
Let P(x) be the statement "x likes subject mathematics," where the domain for x consists of all students. Express each of these quantifications in English. a) ∃
(a).\exist:∃: There exist
Two Balls are to be selected without replacement from a bag that contains one red, one blue, one green and one orange ball. A) Use the counting principle to determine the number of possible points in the sample space. Construct …
Mark and Erik are to play a tennis tournament. The first person to win two games in a row or who wins a total of three games wins the tournament. Find the number of ways the tournament can occur.
Teams A and B play in a tournament. The first team to win three games wins the tournament. Find the number n of possible ways the tournament can occur.
There are four roads from city X to Y and five roads from city Y to Z, find (i) how many ways is it possible to travel from city X to city Z via city Y. (ii) how different round trip routes are there from city X to Y to Z to Y a…
Three persons enter into car, where there are 5 seats. In how many ways can they take up their seats?
1. Let p and q be the propositions "Swimming at the Corregidor Island shore is allowed" and "Sharks have been spotted near the shore," respectively. Express each of these compound propositions as an English sentence.
Let A = {2, 3, 5, 7, 11, 13} and B = {A, 2, 11, 18}. 1. Find A ∪ B. 2. Find A ∩ B. 3. Find A − B.
Let A = {x ∈ R : x 2 = 2} and B = {x ∈ R : x ≥ 0}. 1. Find A ∩ B. 2. Find A ∪ B. 3. Find A − B. 4. For U = R, find Ac and Bc . 5. Find N − B.
There are 21 pupils in a grade 7 class. The class teacher has to choose eight of the pupils for a group that will visit Germany in three months time. In how many different ways can the teacher select pupils for the group ?
If the truth value of p is "false", the truth value of q is "false", and the truth value of r is "true", which of the following expressions is "false"?
Determine whether each of these functions from {a,b,c,d} to itself is one-to-one. a) f(a)=b, f(b)=a, f(c)=c, f(d)=d
State whether the null hypothesis should be rejected on the basis of given P-value. P-value 0.002, a 0.01, one-tailed test.
Find the solution of the recurrence relation an = 4an−1 − 3an−2 + 2 n + n + 3 , a0 = 1 and a1 = 4
Determine the cardinality of the power set of the set {2,3,x,y,z}
Let={2,4,7},B={2,5,4} find the set A∆B
Let A = { y € Z | y = 10b - 3 for some integer b } B = { z € Z | z = 10c + 7 for some integer c } Prove or Disprove that A = B
Define group. Show that the set P3 of all permutations on three symbols 1,2,3 is a finite non-abelian group of order six with respect to permutation multiplication as composition.
Consider a relation R=\ (1,1),(1, ), (0,2), (2,3) (3,1)) on the set A=\ 1,2,3\ Find transitive closure of the relation R using algorithm Warshall's
Find matrix and digraph of the relation R=\ (x,y)/xRy iff 2+y is every defined on the set A=\ 1,2,3,4\
Define Semigroup and Monoid. Show that the set of positive Integer is a monoid for the operation defined by aOb = max{ a,b}.
Proof that an undirected graph has an even number of vertices of odd degree.
Express the given proposition using P,Q,R loyal connectives P:you are sick Q:you miss tha examination R: you pass this subject You did not miss the examination if and only if you pass the subject
The English alphabet contains 21 consonants and fivevowels. How many strings of six lowercase letters of theEnglish alphabet contain: a) exactly two vowels? b) at least two vowels?
Show that a lattice is distributive if and only if for any elements a,b,c in thee lattice (aVb) V c< aV (bVc)
Define a relation - on the set of real numbers by x-ymeans I x | + I y I : I x+y l. which of the properties for an equivalence relation does - satisfy?
Define a relation R on {a,b,c, int i* e . a Reflexive but not symmetric ↳ Symmetric but not transitive <> Transitive but not reflexive
the transitive closure of a binary relation R on a set X is the smallest relation on X that contains R and is transitive steps of Warshall's Algorithm: Step 1: Execute W:=M_R, k:=0W:=M R ​ ,k:=0 Step 2: Execute k:=k+1k:=k+1 S…
Consider a relation R= {(1, 1) (1, 3), (2, 2), (2,3) (3,123 on the set A = {1,2,37 Find transitive using warshalls algorithm... closure of the relation R consider
Consider a relation R= {(1, 1) (1, 3), (2, 2), (2,3) (3,1)on the set A = (1,2,3) Find transitive using warshalls algorithm... closure of the relation R consider
Consider two sets A and B such that A ⊆ B. Find the possible values of x if A = {2, 4, 6, x} and B = {2, 3, 5, 6, x+1}. Ans: x = 3. Please explain.
As for those three guys, John, Bill and Bob, I will only vote for one. Translate into proposition logic.
) How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other?
Determine whether f : Z × Z → Z is onto if f(m,n)= m-n
Let R={(1,2),(2,1),(2,3),(3,4),(4,1) } be a relation on the A={1,2,3,4}. Find the transitive closure of R using Warshall's algorithm.
Let A consist of all 52 cards in an ordinary deck of playing cards. Suppose that this deck is shuffled and a hand of five cards is dealt. A list of cards in this hand, in the order in which they were dealt, is a permutation of A…