Q: Does the word "appointment" mean the same thing in "I'm leaving work early because I have a doctor's appointment." and "He erred by the appointment of unsuitable men."?

A: different meanings

Q: Does the word "touch" mean the same thing in "The cooling touch of the night air." and "There was a touch of sarcasm in his tone."?

A: different meanings

Q: Does the word "think" mean the same thing in "I think she is pretty, contrary to most people." and "I think that he is her boyfriend."?

A: the same meaning

Q: Does the word "know" mean the same thing in "I know that the President lied to the people." and "I know it's time."?

A:
the same meaning