DeMorgan's Theorems Quiz

16 Questions

What do DeMorgan's theorems help with in Boolean algebra?

Simplifying expressions with inverted variables

According to DeMorgan's Theorem (16), what is the equivalent of inverting the OR sum of two variables?

Inverting each variable individually and then ANDing them

What is the equivalent of inverting the AND product of two variables according to DeMorgan's Theorem (17)?

Inverting each variable individually and then ORing them

How can DeMorgan's theorems be applied when x and y are expressions containing more than one variable?

They are equally valid for situations where x and/or y are expressions containing more than one variable

When applying DeMorgan's Theorem (16), which expression can be simplified using ANDing of inverted variables?

(x + y)'

What is the result of applying DeMorgan's Theorem (17) to the expression (xy)'?

(x' + y')

What is the result of applying DeMorgan's Theorem (16) to the expression (A + B)?

A + B'

Using DeMorgan's Theorem (17), what is the equivalent of inverting the AND product of two variables A and B?

A' # B'

Using DeMorgan's Theorem (16), what is the simplified form of the expression (AB + C)'?

(AB)' + C'

How can DeMorgan's Theorems be extended to more than two variables?

By breaking the larger inverter signs at any point in the expression and changing the operator sign to its opposite

What is the output of a NOR gate with inputs x and y, as per theorem (16) of DeMorgan's Theorems?

(x + y)'

According to DeMorgan's Theorems, what can be applied to reduce an expression?

Break an inverter sign at any point in the expression and change the operator sign at that point to its opposite

What does DeMorgan's Theorem (17) state about inverting an AND product?

It is equivalent to ORing the inverted variables

What is the equivalent of inverting the expression (x + y) according to DeMorgan's Theorem (16)?

(x · y)'

When using DeMorgan's Theorems, how can a large inverter sign be broken down?

At any point in the expression and change the operator sign at that point to its opposite

If y = AD + ABD, how can this expression be simplified using DeMorgan's Theorems?

A'B(D' + BD)

Study Notes

DeMorgan's Theorems in Boolean Algebra

DeMorgan's theorems help in simplifying Boolean algebra expressions by breaking down complex statements into simpler ones.
The equivalent of inverting the OR sum of two variables is the AND product of their inverses, i.e., (x + y)' = x' y'.
The equivalent of inverting the AND product of two variables is the OR sum of their inverses, i.e., (xy)' = x' + y'.
DeMorgan's theorems can be applied to expressions containing more than two variables by recursively breaking down the expressions into smaller ones.
The expression (x' y')' can be simplified using ANDing of inverted variables.
Applying DeMorgan's Theorem (17) to the expression (xy)' results in x' + y'.
Applying DeMorgan's Theorem (16) to the expression (A + B) results in A' B'.
The equivalent of inverting the AND product of two variables A and B is A' + B'.
The simplified form of the expression (AB + C)' is A' B' + C'.
DeMorgan's Theorems can be extended to more than two variables by recursively applying the theorems.
The output of a NOR gate with inputs x and y is x' y', as per DeMorgan's Theorem (16).
DeMorgan's Theorems can be applied to reduce an expression by breaking down complex statements into simpler ones.
DeMorgan's Theorem (17) states that inverting an AND product is equivalent to the OR sum of their inverses.
The equivalent of inverting the expression (x + y) is x' y'.
A large inverter sign can be broken down into smaller ones using DeMorgan's Theorems.
The expression y = AD + ABD can be simplified using DeMorgan's Theorems by breaking down the expression into smaller ones.

Test your knowledge of DeMorgan's theorems, which are important in simplifying Boolean algebra expressions. This quiz covers the concepts and applications of Theorems 16 and 17.

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