Math Problem! Set and negation

[chin]

J.K. Rowling (the author of Harry Potter) defines human into two
sets, wizards and muggles as shown below:

Wizards = {Harry Potter, Ron Weasley, Hermione Granger}
Muggles = {Vernon Dursley, Aunt Petunia, Durley Dursley}

(a)Find the number of subsets of the muggles that defined.
(b)Write the negation of this statement:
“If Durley is a wizard, he would probably play magic.”
(c)In the world of wizardry, the wizards can be defined into three
sets, pure-blood, half-blood and mud-blood. If the set of half-blood
has 255 proper subsets, how many elements are there in the set?

 

[pka]

(a)Find the number of subsets of the muggles that defined.
If a set has n elements then it has 2<SUP>n</SUP> subsets.
However, I doubt that the empty set counts as a set of muggles.
So substract 1.

(b)Write the negation of this statement:
“If Durley is a wizard, he would probably play magic.”
The negation of “If P then Q” is “P and not Q”.

(c)In the world of wizardry, the wizards can be defined into three
sets, pure-blood, half-blood and mud-blood. If the set of half-blood
has 255 proper subsets, how many elements are there in the set?
2<SUP>n</SUP>−1=255 has what solution for n?

 

[soroban]

Hello, chin!

J.K. Rowling (the author of Harry Potter) defines human into two
sets, wizards and muggles as shown below:

Wizards = {Harry Potter, Ron Weasley, Hermione Granger}
Muggles = {Vernon Dursley, Aunt Petunia, Durley Dursley}

(a) Find the number of subsets of the muggles that defined.

A set with n elements has 2ⁿ subsets.
. . [It has 2ⁿ - 1 <u>proper</u> subsets.]

There are 3 muggles; there are: 2³ = 8 subsets.

(b) Write the negation of this statement:
“If Durley is a wizard, he would probably play magic.”

The negation of "If p, then q" is: "p and not q".

"Durley is a wizard <u>and</u> he would probably <u>not</u> play magic."

(c) In the world of wizardry, the wizards can be defined into three
sets, pure-blood, half-blood and mud-blood.
If the set of half-blood has 255 proper subsets, how many elements are there in the set?

Recall that a set of n elements has 2ⁿ - 1 proper subsets.

. . We have: .2ⁿ - 1. = .255 . ---> . 2ⁿ .= .256 . ---> . n = 8

There are 8 half-bloods.

. . (Edit: Too fast for me, pka!)