Meaning : Set up or found.

Example : She set up a literacy program.

Synonyms : found, launch, set up

Meaning : Set up or lay the groundwork for.

Example : Establish a new department.

Synonyms : constitute, found, institute, plant

Meaning : Establish the validity of something, as by an example, explanation or experiment.

Example : The experiment demonstrated the instability of the compound.
The mathematician showed the validity of the conjecture.

Synonyms : demonstrate, prove, shew, show

Meaning : Institute, enact, or establish.

Example : Make laws.

Synonyms : lay down, make

Meaning : Bring about.

Example : The trompe l'oeil-illusion establishes depth.

Synonyms : give

Meaning : Place.

Example : Her manager had set her up at the Ritz.

Synonyms : instal, install, set up

Meaning : Build or establish something abstract.

Example : Build a reputation.

Synonyms : build

Meaning : Use as a basis for. Found on.

Example : Base a claim on some observation.

Synonyms : base, found, ground