Logic

Question 1

Equivalent statements:

All A are B
Some A are B
No A are B
Some A are not B

Answer 1

There are no A that are not B
There is at least one A that is B
All A are not B
Not all A are B

Question 2

What words mark an equivalent statement? (3)

Answer 2

All, no, some

Question 3

Negations:

All A are B
Some A are B

Answer 3

Some A are not B
No A are B

Question 4

Simple vs compound statements

Answer 4

Simple: one idea, no connective words
Compound: >1 idea, connective word (typically and)

Question 5

What does disjunction mean?

Answer 5

OR statement

Question 6

What is a conditional statement? Other terms for words?

Answer 6

Conditional = if-then or antecedent-consequent

Question 7

3 other forms of if-then?

Answer 7

Is sufficient/necessary for, only if

Question 8

What is a biconditional statement?

Answer 8

If both if-then and inverse are true (INVERSE MAY NOT NECESSARILY BE TRUE)

Question 9

What is the order of connectives? (Most-least dominant)

How do we group statements?

Answer 9

Biconditional/conditional/AND and OR/negation

Group AROUND (front and back of) most dominant connective

Question 10

Note about truth of conditionals?

Answer 10

If P = false, can’t say much about q, so we default to true.

Question 11

How to make a truth table for

if p then q
not p
————
therefore not q

Answer 11

p and q, not p and not q, if p then q, combine top, combine top and bottom.

Question 12

How to spot invalid arguments?

Answer 12

If any row in table where all premises true, but conclusion still false.

Question 13

How to determine #rows in truth table?

Answer 13

2^n where n = number of simple statements

ie p/q/r = 2^3 =8 rows