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Chapter 1.2

School

Brandeis UniversityDepartment

Computer ScienceCourse Code

COSI 29aProfessor

Cherniack MitchChapter

1.2This

**preview**shows half of the first page. to view the full**2 pages of the document.**Chapter 1.2 Outline

Propositional Equivalences

Pages 20 – 28

Logic and Bit Operations

A 1 bit represents true and a 0 bit represents false. Often, programs represent as OR, as

AND, and ⨁ as XOR.

A bit string is a sequence of bits, and the length of the string is the number of bits in the string.

The bitwise operations are the bit operations of bit strings.

Ex: The bitwise operations of two strings are shown:

0110110110

1100011101

___________

1110111111 bitwise OR

0100010100 bitwise AND

1010101011 bitwise XOR

Logical Equivalences

A compound proposition that is always true is called a tautology.

A compound proposition that is always false is called a contradiction.

A proposition that is neither is a contingency.

Ex: p ⋁ ¬p is a tautology. p ¬p is a contradiction.

Propositions p and q are logically equivalent if p ↔ q is a tautology.

Logically equivalent propositions are denoted as p ≡ q. Also, it can be denoted as p ⟺ q.

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