A. Notes

*DeMorgan’s Law** *tells us how to negate a combined statement such as A OR B, and A AND B.

**NOT (A OR B) = NOT A AND NOT B i.e. ~ ( A + B ) = ~A * ~B **

** **** **

**NOT (A AND B) = NOT A OR NOT B i.e. ~( A * B) = ~A + ~B**

Here, A and B can be any statement such as "Noah eats more apples than Justin" or "x < 3"

B. HW Practice

1. Let A be " x<3" and B be " x >10" , draw a number line, color all numbers less than 3 **red**, and all number greater than 10 **blue**, and the rest **yellow**. What is the color of a number that is A OR B? What is the color of a number that is NOT(A OR B)? What is the color of a number that is "NOT A AND NOT B"?

2. Let A be " x<3" and B be " x >10" , draw a number line, color all numbers less than 3 **red**, and all number greater than 10 **blue**, and the rest **yellow**. Can you find a number that is A AND B? Can you find a number that is NOT(A AND B)? Can you find a number is "NOT A OR NOT B"?

3. Can you think of another example similar to the above to prove DeMorgan's Law? For instance, you can assume that A is " y > 0" and B is " y < 5". What do **~ ( A + B ) **and** ~A * ~B **mean then? Are they always equivalent? What do **~( A * B) **and** ~A + ~B **mean? Are they always equivalent?

4. Simply the following:

~ (A + B) + ~(A + ~B)

~ (A * B) + ~(A * ~B)

red or blue, yellow,yellow

N/A, y, y

any number, yes, ay number >0,<5

TRUE, true

yellow, yellow

no, yes, yes

not a and b, yes, not a and not b, no

true, false