1. Using Truth Table prove that:

a) (A B) = AB + AB

b) (A B) = AB + AB

2. Simplify the following expression by using the simplification theorem. You should be able to simplify this to two product terms.

F = AB + ABC + ABC + ACD

Hints: You may have to use multiple simplification theorems. Try one at a time.

3. Use DeMorgans Theorem to obtain SOP expression for each of the following:

a) ( (x + z)(xy )

b) ( (xy) (y + z))

4. Given 4 input variables: A, B, C and D.

Find out the algebraic expressions of the following minterms and maxterms.

a) m9

b) M11

c) m5

d) M7

e) m13

5. Given the following Truth Table.

ABCF

0001

0010

0100

0111

1000

1010

1101

1111

a) Determine the minterm expansion for the function F

b) Determine the maxterm expansion for the function F

c) Simplify the minterm expansion to get the minimum SOP. (Use Simplification theorem)

6. Using the following Truth Table, (a) Find out the maxterm expansion for the function F

ABCF

0000

0011

0101

0111

1000

1010

1100

1111

And then simplify the maxterm expansion to get a minimum POS. (Use simplification theorems)