W1 Sets Sequences, Integers, Matrices

Question 1

Z N Q R what represent?
what are their relationship

Answer 1

Z:Zahlen整数(-3,-2,-1,0,1,2,3)
N: 0,1,2,3
Q:quotient p/q, p∈Z, q∈N
R: real

N⊊Z⊊Q⊊R
new zealand qantas route

Question 2

S ⊆ T , S⊊T 区别?

Answer 2

S⊊T if S⊆ T ∧ S≠T

Question 3

{a} ⊆ { {a} } ?
{a} ∈ { {a} } ?

Answer 3

no because a ∉ { {a} }
yes because {a} is an element of { {a} }

Question 4

let S be a finite set. cardinality of P(S) 是?

Answer 4

|P(S)|=2^|S|

Question 5

|∅|=?

Answer 5

0

Question 6

A: {1,2,1,{1}} |A|=?

Answer 6

3 重复的1不算

Question 7

A ⊆ A?

Answer 7

yes since every set is subset of itself.

Question 8

A is a set and B={A, {A}}, A⊆B?

Answer 8

NO
since A and {A} are elements of B, we have A ∈ B and {A} ∈ B. It follows that {A} ⊆ B and {{A}} ⊆ B. However, it is not true that A ⊆ B.

Question 9

Let A = {1, 2, 4, a, b, c}.
∅ ∈ A ? give T/F

Answer 9

F

Question 10

Let A = {1, 2, 4, a, b, c}.
{ } ∉ A ? give T/F

Answer 10

T

Question 11

Let A = {1, 2, 4, a, b, c}.
A ∈ A

Answer 11

F
it is T that A ⊆ A

Question 12

Let A = {1, {2, 3}, 4}
{1,4} ⊆ A?

Answer 12

T

Question 13

Let A = {1, {2, 3}, 4}
{2, 3} ⊆ A?

Answer 13

F

Question 14

what is A-B
what is B-A
what is A\B
what is B\A
if A B represent hobbies of A , B

Answer 14

A-B : the set of all x that are in A but ￢ in B
A 的独有兴趣
B-A: the set of all x that are in B but ￢ in A
B 的独有兴趣

Question 15

what is
__
A

Answer 15

complement of A
U-A

Question 16

what is
A ⊕ B

Answer 16

symmetry difference.
means (A-B) ∨ (B-A)
两个人独有兴趣的结合，排除了他们共同的兴趣。