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Show that a lattice is distributive if and only if for any elements a,b,c in thee lattice (aVb) V c< aV (bVc)
show that ~Q,P—>Q=>~P in mathematical foundations of computer science
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?
Find the sum-of-products expansions the Boolean function F(x, Y, 2) that equals 1 if and only if
a)x = 0.
b) xy = 0.
c) x +y = 0.
d)xyz = 0.
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
Construct a K-map for F(x, y, z) = xz + yz + xyz. Use this K-map to find the implicants, prime
implicants, and essential prime implicants of F(x, y, z).
Proof that an undirected graph has an even number of vertices of odd degree.
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.
Define Semigroup and Monoid. Show that the set of positive Integer is a monoid for the operation
defined by aOb = max{ a,b}.
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\
