P is determined by three logical variables X, Y and Z. For every possible combination of X, Y and Z, the truth table gives the corresponding value of P..

Construct compound proposition p according to truth table.

For each variable x, y, z, the compound proposition p is true, that is, the combination of P= 1

For example, in our truth table, the combination of P= 1 is:

X=0，Y=0，Z=0

X=0，Y= 1，Z=0

X=0，Y= 1，Z= 1

X= 1，Y=0，Z=0

X= 1，Y=0，Z= 1

Use the variables x, y, z or their negation? x，？ y，？ Z as a conjunction, such as:

For X=0, Y=0, Z=0, the conjunction is:? x？ ∧Y？ ∧Z

For X=0, Y= 1, Z=0, the conjunction is:? x？ ∧ Y？ ∧Z

For X=0, Y= 1, Z= 1, the conjunction is:? x？ ∧ Y？ ∧ Z

For X= 1, the conjunction of Y=0 and Z=0 is: x? ∧ ? y？ ∧Z

For X= 1, Y=0, Z= 1, the conjunction is: x? ∧ ? y？ ∧ Z

Then extract all conjunctions, namely:

(? x？ ∧Y？ ∧Z) ∨？ (? x？ ∧ Y？ ∧Z)？ ∨? (? x？ ∧ Y？ ∧ Z)？ ∨? (X？ ∧Y？ ∧Z)？ ∨? (X？ ∧Y？ ∧ Z)

Regarding functional integrity:

A set of logical operators, such as the ones we used above: AND ∧, or ∨, NOT? These three operators.

All compound propositions can be derived from these three operators, so they form a set of fully functional operators.

Similar full-featured operators are:

NAND: Because "or" can be represented by "NAND": X? ∨ Y =(？ x？ ∧Y)

NOR: Because AND can be represented by NOR: X? ∧? Y =(？ X ∨Y)

……