Question

SIMPLIFY THE FOLLOWING USING BOOLEAN THEOREMS OR DE MORGAN’S LAW INCLUDING STEPS:

Answer 1

Answer:De Morgan's theorem

De Morgan's theorem states (Equation 1.16) that complementing the result of OR'ing variables together is equivalent to AND'ing the complements of the individual variables. Also (Equation 1.17), complementing the result of AND'ing variables together is equivalent to OR'ing the complements of the individual variables.

Example 1.9

Use Boolean algebra and de Morgan's theorem for two variables,

¯

A+B

=

ˉ

A

⋅

ˉ

B

, to show that the form given in Equation 1.16 for three variables is also true.

Solution

¯

A+B+C

=

¯

(A+B)+C

  associative law

=(A+B)⋅

ˉ

C

    De Morgan′s theorem

=(

ˉ

A

⋅

ˉ

B

)⋅

ˉ

C

      De Morgan′s theorem

=

ˉ

A

⋅

ˉ

B

⋅

ˉ

C

          associative law

Example 1.10

Draw the circuits that will perform the functions described by both sides of the first of De Morgan's theorems (Equation 1.16) given in Table 1.4, and also demonstrate the theorem is true using a truth table.

Explanation:

Answer 2

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She created the National Women's Party, which was known for bold protests.