Exploring Boolean Logic and De Morgan's Theorem

What are the basic Boolean operations?

• NAND, NOR, XNOR

• AND, OR, XOR

• AND, OR, NOT

• AND, OR, IF

Construct a truth table for the expression A AND B.

• A OR B Truth Table

• A AND B Truth Table: A | B | A AND B T | T | T T | F | F F | T | F F | F | F

• A AND NOT B Truth Table

• A NAND B Truth Table

What is the result of A OR NOT A?

• undefined

• null

• false

• true

State the commutative law of Boolean algebra.

• A + B = B + A and A · B = B · A

• A + B = A and A · B = B

• A + B = A · B and A · B = A + B

• A + B = A + A and A · B = B · B

How many rows are in a truth table for two variables?

• 2

• 6

• 4

• 8

What does De Morgan's theorem state about conjunctions?

• The negation of a conjunction is equivalent to the disjunction of the negations.

• The negation of a conjunction is equivalent to the conjunction of the negations.

• The conjunction of two negations is equivalent to the negation of their disjunction.

• The disjunction of a conjunction is equivalent to the negation of the conjunction.

Simplify the expression A AND (B OR C).

• A AND B AND C

• A OR C

• A AND (B OR C)

• A OR (B AND C)

What is the identity law in Boolean algebra?

• A AND A = 1; A OR A = 0

• A AND 1 = 0; A OR 0 = 1

• A AND 1 = A; A OR 0 = A

• A AND 0 = A; A OR 1 = A

Construct a truth table for the expression A OR B AND C.

• | A | B | C | B AND C | A AND (B AND C) |

• | A | B | C | B AND C | A AND (B OR C) |

• | A | B | C | B OR C | A OR (B OR C) |

• | A | B | C | B AND C | A OR (B AND C) | |---|---|---|---------|----------------| | T | T | T | T | T | | T | T | F | F | T | | T | F | T | F | T | | T | F | F | F | T | | F | T | T | T | T | | F | T | F | F | F | | F | F | T | F | F | | F | F | F | F | F |

What is the result of NOT (A AND B)?

• A AND B

• (NOT A) OR (NOT B)

• A OR B

• NOT A