USC Logic Web — Unit II: Syntax

Exercises on use and mention, the vocabulary of propositional logic, and construction trees.

Use and Mention

1.1

Los Angeles designates a city in the West Coast.

‘Los Angeles’ designates a city in the West Coast. ‘Los Angeles’ designates a city in the ‘West Coast’. Los Angeles ‘designates’ a city in the West Coast. ‘Los Angeles’ designates ‘a city’ in the West Coast.

1.2

Snow is white is not is not a grammatical sentence of English.

‘Snow is white’ is not is not a grammatical sentence of English. ‘Snow is white is not’ is not a grammatical sentence of English. ‘Snow is white’ is ‘not’ is not a grammatical sentence of English. ‘Snow is white is not is not’ a grammatical sentence of English.

1.3

What is monosyllabic but whatever is polysyllabic.

‘What is monosyllabic’ but ‘whatever is polysyllabic’. ‘What’ is monosyllabic but whatever is polysyllabic. ‘What’ is monosyllabic but ‘whatever’ is polysyllabic. ‘What’ is ‘monosyllabic’ but ‘whatever’ is ‘polysyllabic’.

1.4

Snow refers to snow. Select any true statements.

Snow refers to ‘snow’. ‘Snow’ refers to ‘‘snow’’. ‘‘Snow’’ refers to ‘snow’. ‘Snow’ refers to snow.

1.5

San Diego in the morning, Santa Barbara in the afternoon, and San Francisco in the evening all start with San. Select any true statements.

‘San Diego’ in the morning, ‘Santa Barbara’ in the afternoon, and ‘San Francisco’ in the evening all start with San. ‘San Diego in the morning’, ‘Santa Barbara in the afternoon’, and ‘San Francisco in the evening’ all start with San. ‘San Diego in the morning’, ‘Santa Barbara in the afternoon’, ‘and San Francisco in the evening’ all start with ‘San’. ‘San Diego in the morning, Santa Barbara in the afternoon’, and ‘San Francisco in the evening’ all start with ‘San’.

Vocabulary

2.1

φ (phi)

Yes No

Construction Trees

Each exercise loads a formula into the formula checker. Switch to the Build tab to construct the parse tree step by step, identifying the main connective at each stage.

Notational Conventions

These expressions omit outer parentheses by convention. Identify the main connective and construct the tree for the corresponding official formula.