# 02 - De Morgans Laws

1. Select which of the following options (1,2,3,4) fits when DeMorgan's laws are applied:
```Note: In this notation the "~" is a 'NOT'

~(A * B) =

1. ~A + ~B

2. ~A * ~B

3. A * B

4. ~A * B ```

3

2

1

4

2. Apply DeMorgan's laws to: ~(A + B) =
```Note: In this notation the "~" is a 'NOT'

~(A + B) =

1. ~A + ~B

2. ~A * ~B

3. A * B

4. ~A * B ```

4

2

3

1

3. DeMorgan’s theorem may be thought of in terms of breaking __________

A + sign

the commutative law

A long bar symbol

the rules of boolean algebra

4. When multiple “layers” of bars exist in an expression, you may only break one bar at a time, and it is generally easier to begin simplification by breaking the longest (uppermost) bar first

FALSE

TRUE

5. Use DeMorgan's law on the expression: DE + ~D + ~E and you will get: DE + D* ~E

FALSE

TRUE

6. You should never break more than one bar in a single step

TRUE

FALSE

7. Fill in the blanks in this excerpt that explains what DeMorgan's Theorems describe
```DeMorgan’s Theorems describe the equivalence
between gates with inverted inputs and gates
with inverted outputs.

Simply put, a NAND gate is equivalent to a
Negative-OR gate, and a NOR gate is equivalent
to a _______________________________```

negative XOR gate

negative - OR Gate

Negative-AND gate.

positive OR Gate

8. DeMorgan's laws: Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and ___________

XOR'ed

AND'ed

OR´ed

further inverted again

9. Analyse the first two steps provided below and fill in the blanks for 1 and 2.

1 = signs 2 = converted

1 = shapes 2 = redirected

1 = signs 2 = OR'ing

1 = shapes 2 = inverted

10. Given that F = A'B'+ C'+ D'+ E', which of the following represent the only correct expression for F'?
`Note: In this notation we use the ' to denote negation`

F'= AB(C+D+E)

F'= (A+B)CDE

F'= A+B+C+D+E

F'= AB+C'+D'+E'

11. What part of this table, on careful analysis, proves that DeMorgan's theorem is correct?

every single column contains at least one '1' which proves the theorem

column no 7 and 8 are equal and column no 9 and 10 are also equal

columns 5,9 and 10 contain only one 0, which proves the theorem

columns 6 and 7 are inverse to each other

12. Not (A and B) is the same as Not A ___ Not B.

and

or

not

nor

13. Read the rather long question below to use DeMorgan's laws to solve this 'real world' problem.
```A recent survey asked high school students whether
or not they planned to go to the upcoming basketball
game or the upcoming football game.

200 total students were surveyed.

58 students stated that they would miss at
least one of the games (this includes the
students that plan to miss both games).

How many students plan to attend both games?

By De Morgan's Laws, this set of 58 students is
the complement of the set of students who will
attend both games.

Therefore, the number of students who will attend
both games is:```

58 - 58 = 0

200 + 58 = 142 and 200 - 142 = 58

200 - 58 = 142

58 + 58 = 116

14. By De Morgan's Laws, A NAND B is equivalent to~A OR ~B (The overline represents the negation of a signal). Thus, an OR gate can be constructed by ______________________

negating each output of an OR gate

inverting each output of an AND gate

inverting each input of an OR or NOR gate

negating each input of a NAND gate.

15. Augustus De Morgan, credited with formulating DeMorgan's laws, was born in _____________ in 1806

London, England