Foundations of mathemtics

Question 1

N

Answer 1

Natural numbers {1,2,3,…}

Question 2

Z

Answer 2

The set of all integers {0,+-1,+-2,+-3,…}

Question 3

Q

Answer 3

The set of all natural numbers

Question 4

R

Answer 4

The set of all real numbers

Question 5

C

Answer 5

The set of all complex numbers {a+bi | a,b c R}

Question 6

|u|

Answer 6

Number of elements in the set u

Question 7

Singleton

Answer 7

A set with one element

Question 8

∅

Answer 8

The empty set

Question 9

What is a PROPER SUBSET

Answer 9

Every element of B is also an element of a but b does not equal A

Question 10

[a,b]

Answer 10

x is greater or equal than a, and less than or equal to b.

Question 11

(a,b)

Answer 11

x is greater than a and less than b.

Question 12

AUB

Answer 12

Union, x is an element of a or an element of b

Question 13

A∩B

Answer 13

Intersection, x is an element of A and of B

Question 14

A\B

Answer 14

Difference, x is an element of A but not an element of B

Question 15

Disjoint

Answer 15

When A and B have no common elements

Question 16

The ordered N-tuple

Answer 16

(x1,x2,x3,…xn) where the position of each element is significant

Question 17

What is the cartesian product of AxB

Answer 17

{(a,b) | a∈A and b∈B}

Question 18

The principle of the excluded third

Answer 18

either P is true, or ˜P is true, there is no third possility

Question 19

Disjunction

Answer 19

P or Q (or in an inclusive sense)

Question 20

Conjunction

Answer 20

P and Q

Question 21

∀

Answer 21

for every, for all

Question 22

∃

Answer 22

there exists

Question 23

Contrapositive

Answer 23

if P imlies Q, it’s contrapositive is that thee negation of P implies th negation of Q

Question 24

1+2+3+….+n=?

Answer 24

n(n+1)/2

Question 25

Image

Answer 25

The image of a function mapping A to B, is the set B

Question 26

Domain

Answer 26

The domain of a function mapping A to B, is the set A

Question 27

Injective

Answer 27

If a1,a2 are elements of A and a1->b and a2->b then a1=a2

one to one function

Question 28

surjective

Answer 28

If f maps A to B every element of B is the image of at least one element of A

Question 29

Bijective

Answer 29

A bijective function is both Injective and surjetive

Question 30

Comutative

Answer 30

xy=yx

Question 31

asociative

Answer 31

x(yz)=(xy)z etc

Question 32

Identity element

Answer 32

ex=xe=x (where e is the identity)

Question 33

Inverse

Answer 33

if xy=yx=e then y is the inverse of x