Discrete Structures Week 1

Question 1

What is a proposition?

Answer 1

a statement that is true or false

Question 2

What is a truth value?

Answer 2

T or F
- the truth value of a proposition is T or F

Question 3

What are logical variables?

Answer 3

propositions are called variables
- represent a proposition with a symbol
- make new propositions out of old ones

Question 4

Negation operator

Answer 4

“not p”
the little corner p

Question 5

principle of noncontradiction

Answer 5

a proposition and its negation cant be true at the same time

Question 6

conjunction operator

Answer 6

“p and q are true”
p ^ q

Question 7

disconjunction operator

Answer 7

“p or q is true (or both)”
p v q

Question 8

truth table, what for, and how to set up

Answer 8

a logical operator is fully determined by its truth table
- the truth values of the operator if we are given the truth values of p and q
1 - 2 ^ propositions
2- 1st row, half true, half false
3- half of half true, half of half false
4- alternating

Question 9

conditional operator

Answer 9

“if p, then q”
p -> q

Question 10

vacuously true

Answer 10

the assumption is false, statement t
p -> q
if p is false
p -> q is t

Question 11

biconditional operator

Answer 11

“p if and only if q”
p <-> q
“if p, then q, and if q, then p”
p -> q ^ q -> p

Question 12

exclusive or operator

Answer 12

XoR
“p or q, but not both”
p “direct sum(plus inside a circle” q

Question 13

equivalence

Answer 13

2 logical operators are equivalent if they have the same truth table

Question 14

equivalence proposition

Answer 14

p <=> q
“p and q are equivalent id p and q have the same truth table”
- asks you to prove, already know they are the same