DE MORGAN LAW EXIT SLIP

Bitwise operators and De Morgan law

​Recap

Identify the logical operators AND, OR, and NOT and construct the truth table for logical operations within a statement or a computer program

Multiple Choice

Which logical operator returns True only if both conditions are True?

• OR

• NOT

• XOR

• AND

Multiple Choice

Which logical operator returns True if at least one condition is True?

• AND

• OR

• NOT

• NAND

Multiple Choice

What is the truth value of the expression "NOT True"?

• True

• False

Objectives

• Implement the correct syntax for a particular bitwise or logical operator according to a given scenario

• Evaluate expressions using De Morgan law by applying it within the code for a given scenario to demonstrate the negation of conjunction and disjunction

Bitwise Operators

• Bitwise operators perform operations on individual bits of binary numbers.

• Common bitwise operators in Python:

  1. AND (&): Sets each bit to 1 if both bits are 1.

  2. OR (|): Sets each bit to 1 if either of the bits is 1.

  3. XOR (^): Sets each bit to 1 if only one of the bits is 1.

  4. NOT (~): Inverts all the bits.

Multiple Choice

Which bitwise operator sets each bit to 1 if both bits are 1?

• AND (&)

• OR (|)

• XOR (^)

• NOT (~)

Multiple Choice

Which bitwise operator inverts all the bits?

• AND (&)

• OR (|)

• XOR (^)

• NOT (~)

Logical Operators

• Logical operators are used to combine multiple conditions.

• Common logical operators in Python:

  1. AND (and): Returns True if both conditions are True.

  2. OR (or): Returns True if at least one condition is True.

  3. NOT (not): Returns the opposite of the condition's result.

Multiple Choice

Which logical operator returns True if both conditions are True?

• AND (and)

• OR (or)

• NOT (not)

Multiple Choice

Which logical operator returns True if at least one condition is True?

• AND (and)

• OR (or)

• NOT (not)

De Morgan's Law - Negation of Conjunction

• De Morgan's Law states that the negation of a conjunction is equivalent to the disjunction of the negations of the individual conditions.

• Example: "not (A and B)" is equivalent to "(not A) or (not B)."

Multiple Choice

What is the negation of the expression "A and B" using De Morgan's Law?

• not A and not B

• not A or not B

• not (A or B)

• not (A and B)

Multiple Choice

Which law states that the negation of a conjunction is equivalent to the disjunction of the negations of the individual conditions?

• Commutative Law

• Associative Law

• Distributive Law

• De Morgan's Law

De Morgan's Law - Negation of Disjunction

• De Morgan's Law also applies to the negation of disjunction (OR).

• Example: "not (A or B)" is equivalent to "(not A) and (not B)."

Multiple Choice

What is the negation of the expression "A or B" using De Morgan's Law?

• not A and not B

• not A or not B

• not (A or B)

• not (A and B)

Multiple Choice

De Morgan's Law also applies to the negation of which logical operator?

• AND (and)

• OR (or)

• NOT (not)

Combining De Morgan's Laws

• De Morgan's Laws can be combined to simplify complex expressions.

• Example: "not (A and B or C)" can be simplified to "(not A) or (not B and not C)."

Multiple Choice

Which laws can be combined to simplify complex expressions using negations?

• Commutative and Associative Laws

• Distributive and De Morgan's Laws

• Identity and Inverse Laws

• De Morgan's and Identity Laws

Multiple Choice

What is the simplified form of the expression "not (A and B or C)" using De Morgan's Laws?

• (not A) or (not B and not C)

• (not A and not B) or (not A and not C)

• (not A and not B and not C)

• (not A or not B) and (not A or not C)