If-Then Statements

What steps do you need to form a true contrapositive?

first reverse then negate

When chaining, what direction do you read from?

Left to right- makes farthest left rule the strongest as it forces every other rule.

How do you contrapose a chain?

Flip the direction (farthest left becomes farthest right) & negate.

Do different branches have a relationship?

NO

BOTH has which possibilities for A & B?

ONE POSSIBILITY: A is true & B is true

Written: A + B

NOT BOTH has which possibilities for A & B?

THREE POSSIBILITIES

1. A is True & B is False

2. A is False & B is True

3. A is False & B is False

A & B CAN NOT BOTH BE TRUE

Written: ~(A+B)

NEITHER has which possibilities for A & B?

ONE POSSIBILITY
A is false & B is false

Written: ~(A/B) OR ~A + ~B

EITHER has which possibilities for A & B?

THREE POSSIBILITIES

1. A is true & B is true

2. A is true & B is false

3. A is false & B is true

A & B CAN NOT BOTH BE FALSE

Written: A/B

What term has a positive trigger & negative result?

Not Both (ex. If Jon, then not Sara)

What does the numeric term “at least one is NOT” stand for?

Not Both

What term has a negative trigger & positive result?

EITHER (ex. If not Jon, then Sara)

How is “BOTH” seen in a sentence?

The term “both” does not need to be included in sentence.

Jon and Sara will….

How is “EITHER” seen in a sentence?

The term “either” does not need to be included.

Jon or Sara will…

What to terms signify they need branching?

BOTH & NEITHER after “then”, and their contrapositive (not both & either after “if”)

What terms can’t be branched?

NOT BOTH & EITHER after “then”, and their contrapositives (both & neither after “if”)

What 4 terms all refer to the “IF” trigger?

each. every, any, all

What rule does this follow? ^^

R —→ Q

R is directly after if

What 2 terms refer to the “if” result?

Only & Only if

What rule does this follow?

R —→ Q

Q is directly after only if

What term means “if not”?

unless

What rule does this follow?

Q —> R

Q is after “unless”and should be negated

Rules of “if and only if”

Q —> R —→ Q