proofs test 1

Question 1

R

Answer 1

real nums

Question 2

z

Answer 2

all integers

Question 3

q

Answer 3

rational nums

Question 4

n

Answer 4

positive integers

Question 5

even def

Answer 5

x = 2n

Question 6

odd def

Answer 6

x = 2n + 1

Question 7

same parity

Answer 7

both odd or even

Question 8

p divides q

Answer 8

p | q

Question 9

prime

Answer 9

only factors are 1 and p

Question 10

composite

Answer 10

p has divisors

Question 11

commutative

Answer 11

p ^ q = q ^ p

Question 12

associative

Answer 12

parentheses can be moved

Question 13

distributive

Answer 13

p distributes

Question 14

idempotent

Answer 14

p ^ p = p

Question 15

domination

Answer 15

p ^ F = F

Question 16

identity

Answer 16

p ^ T = p

Question 17

negation

Answer 17

p ^ ~p = F

Question 18

absorption

Answer 18

p OR q ^ p = p

Question 19

contrapositive

Answer 19

p ➝ q = ~q ➝ ~p

Question 20

conditional as “or”

Answer 20

p ➝ q = ~p OR q

Question 21

“and” implies “or”

Answer 21

tautology

Question 22

A subset of B

Answer 22

every element of A is in B

Question 23

power set of A

Answer 23

all subsets in A

Question 24

complement of A

Answer 24

elements present in universal set but not A

Question 25

intersection of A and B

Answer 25

only elements overlapping in A and B

Question 26

union of A and B

Answer 26

adding together A and B

Question 27

A and B are disjoint

Answer 27

intersection of A and B is empty

Question 28

subtract set B from A

Answer 28

A/B

Question 29

symmetric difference of A and B

Answer 29

A\B combined with B\A

Question 30

cartesian product of a and b

Answer 30

multiply to get coordinates of A and B