MINTERM ,CANONICAL SUM OF PRODUCTS(SOP) and MINIMUM SOP

MINTERM:
A minterm is a product term that contains all the variables of a logical function either in true or inverted state.

A logical function is given:
F=AB'+C'

Its truth table is as below:

A  B C F
0 0         0        1
0 0 1        0
0 1         0        1
0 1         1        0
1 0         0        1
1 0         1        1
1 1         0       1
1 1        1        0

All the minterms that can be generated from the above given truth table are:

A'B'C' , A'B'C , A'BC' , A'BC , AB'C' , AB'C , ABC' , ABC

CANONICAL SOP:
It is an expression that describes a logical function from its truth table.A canonical SOP consists of the sum of all the minterms for which the function has a value 1...or the function is true.

For the same truth table as stated above ,the canonical SOP can be written as:
F=A'B'C'+A'BC'+AB'C'+AB'C+ABC'

MINIMUM SOP:
A minimum minterm is obtained by simplifying a canonical SOP. It provides a minimum hardware simplification of the logic function.
For the same truth table,the minimum SOP obtained after simplification is:

F=AB'+C'

"AND", "OR", "NOT" IMPLEMENTATION USING "NOR" GATE

Conversion of a NOR gate into a NOT gate, an OR gate and an AND gate is as shown below:

NOR IMPLEMENTATION

"AND", "OR", "NOT" IMPLEMENTATION USING "NAND" GATE

Conversion of a NAND gate into an AND gate ,a NOT gate and an OR gate is as shown below:

NAND IMPLEMENTATION

UNIVERSAL GATES

NAND and NOR are the universal gates.
AND , OR and NOT are fundamental gates,together they can  implement any digital logic.But NAND or NOR alone is capable enough to implement any digital logic,hence these two gates are called universal Gates.