I. Brainstorming

How many semantic relations of sentence do you know?

II. Semantic relations of sentences

Logicians and formal semanticists study under what circumstances a sentence is true. Those circumstances are called truth conditions.

 X is Tautology: The bachelor is unmarried.

The sentence is necessarily true. The rheme does not provide any new information. 

 X is contradiction: The bachelor is married.

The sentence is necessarily false; the theme and the rheme are incompatible.

 X is inconsistent with Y: John is single./John is married.

If John refers to same person, one sentence is true and the other must be false.

 X is synonymous with Y: John broke the glass./The glass was broken by John.  One is true, the other also is true. One is paraphrase of the other.

 X entails Y: The meeting was chaired by a spinster./The meeting was chaired by a woman.

If one is true, the other is automatically true.

 X presupposes Y: Sam has returned the book./Sam borrowed the book.

One sentence is part of the assumed background against which the other is said

These semantic relations are found within or between meaningful sentences. There are sentences which sound grammatical but meaningless. These sentences are said to be semantically anomalous. For example:

Colourless green ideas sleep furiously. 

The pregnant bachelor killed some phonemes.