Discrete Math Questions

what is logically equivalent to ~(p ⇒ q)

what is logically equivalent to ~(∀x in D, ∃y in E such that P(x, y))

what does it mean if the domain is an empty set for a universal statement

what is logically equivalent to ~(∀x∈ D, Q(x))

proportionality statement of a power (exponential) relationship and what it looks like before propagated

proportionality statement of a root relationship and what it looks like before propagated

proportionality statement of an inverse relationship and what it looks like before propagated

Effet commun sachant celui du milieu

Effet commun ne sachant pas celui du milieu

Chaîne causale ne sachant pas celui du milieu

Chaîne causale sachant celui du milieu

Cause commune sachant celui du milieu

Cause commune ne sachant pas celui du milieu

You want to set a password of length 8, where each position iseither a lower-case English letter or a number from 0 to 9.How many unique passwords can be set?

Let A and B be finite sets. How many distinct functions can be defined with the domain A and co-domain (or range) B?Let sets A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4}.

list all the prime numbers found, using the highest exponent found for each of the integers to find LCM for.- LCM (8, 9)

There are 63 male students, and 73 female students in a class. Howmany ways can we choose a male class rep and a female class rep?

Eight people walk into a cafe to get lunch, where the menu has 12 lunch options. (Assume that each person orders 1 lunch option.)b) Suppose three of the eight people are vegetarians, and two only want to have their lunch with meat. Out of the 12 lunch options, there are 3 vegetarian options. How many possible ways can the eight people order food?

Suppose there are 5 pigeons and 4 pigeonholes, there is always at least one hole

A winery offers tasting of 5 varieties of wines: (R)iesling,(S)auvignon Blanc, (C)hardonnay, (P)inot Gris and (M)erlot. In howmany different orders can a customer taste all these wines?