CS 2100 Module 1: Logic

Question 1

What is a proposition?

Answer 1

A statement that can be either true or false nothing else
ex 7 = 5

Question 2

What is a proposition?

Answer 2

a statement with an ambiguous value or an x

Question 3

How do we represent propositions?

Answer 3

We use propositional variables, denoted by
lowercase letters, to represent propositions.

ex p = “Today is Wednesday”

Question 4

Logical operators

Answer 4

combine propositions, Not, And, Or

Question 5

Not operator

Answer 5

L, turned 270 degrees, flips argument, true if false, false if true

Question 6

And operator

Answer 6

^ , both are true false otherwise

Question 7

Or operator

Answer 7

v, at lease one argument is true, can be both true

Question 8

Or Exclusive

Answer 8

p or q but not both
(p ^ !q) v ( !p ^ q )

Question 9

Operator precedence

Answer 9

1. not
2. and
3. or

Question 10

English But Translation

Answer 10

The same as and operator

Question 11

English neither-nor Translation

Answer 11

not p and not q

Question 12

Less than or equal to: Translation

Answer 12

a <= b = (a<b) v (a=b)
a <= b <= c = (a <= b) ^ ( b <= c)

Question 13

What are truth tables?

Answer 13

It tells all possible true values of any compound statement.

Question 14

Truth Table Not

Answer 14

p: T, f
!p: F, T

Question 15

Truth Table And

Answer 15

p: T, T, F, F
q: T, F, T, F
p ^ q: T, F, F, F

Question 16

Truth Table Or

Answer 16

p: T, T, F, F
q: T, F, T, F
p ^ q: T, T, T, F

Question 17

Logical equivalence

Answer 17

if two statements convey the same logical meaning, or the same value for every row on the truth table, represented by three parallel lines

Question 18

Logic Laws

Answer 18

t = tautology(always true), c = contradiction(always false)
See useful images.

Question 19

Substitution rule

Answer 19

We can replace the expression on the left of = with the expression on the right without changing the truth value

Question 20

tautology

Answer 20

always true

Question 21

contradiction

Answer 21

always false

Question 22

Predicate Logic

Answer 22

use variables instead of blanks to form a predicate
x is a CS Major
becomes proposition when x is known

Question 23

Predicate Domain

Answer 23

Values we use to replace x
Domain of
x is a CS Major
is all students in UoU

Question 24

Element of

Answer 24

represented as a curvy E
a set (domain)
Sarah E D
means Sarah is a n element od the domain D