For each of these statements find a domain for which the statement is true and a domain for which the statement is false. a) Everyone speaks Hindi. b) There is someone older than 21 years. c) Every two people have the same first name. d) Someone knows more than two other people.

a) Everyone speaks Hindi

True Domain: Everyone in Uttar Pradesh (This makes the statement true as everyone cannot speak hindi, but everyone in Uttar Pradesh, an Indian community of indian people can speak Hindi

False Domain: Everyone in the New Jersey (This makes the statement false, as not everyone in New Jersey, which is in the United States can speak Hindi. Probably Indians in New Jersey can speak Hindi, but not everyone

b) There is someone older than 21 years

True Domain: All students in college (This makes it true because there is always someone older than 21 years from all the students in college since many students are over 21 years of age)

False Domain: All the kids in Kindergarten (This statement is false because children in kindergarten are usually between the ages of 2 and say 7 or 8. Hence there is no way to find someone older than 21 years in this domain)

c) Every two people have the same first name

True Domain: Michael Scoffield, Michael Ballack, Michael Owen, Michael Oliver (This is true for this domain since everyone in the domain has the same first name)

False Domain: All the teenagers in the world (The statement is false for this domain because we can find so many first names from this domain)

d) Someone knows more than two other people

True Domain: All the people in the world (From all the people in the world, you can always find someone who knows more than two other people in the world)

False Domain: Everyone living alone in an island that is uninhabited (An uninhabited island means that someone lives alone there and hence he or she cannot know more than two other people since he is alone)

Explanation:

a) Everyone speaks Hindi

True Domain: Everyone in Uttar Pradesh (This makes the statement true as everyone cannot speak hindi, but everyone in Uttar Pradesh, an Indian community of indian people can speak Hindi

False Domain: Everyone in the New Jersey (This makes the statement false, as not everyone in New Jersey, which is in the United States can speak Hindi. Probably Indians in New Jersey can speak Hindi, but not everyone

b) There is someone older than 21 years

True Domain: All students in college (This makes it true because there is always someone older than 21 years from all the students in college since many students are over 21 years of age)

False Domain: All the kids in Kindergarten (This statement is false because children in kindergarten are usually between the ages of 2 and say 7 or 8. Hence there is no way to find someone older than 21 years in this domain)

c) Every two people have the same first name

True Domain: Michael Scoffield, Michael Ballack, Michael Owen, Michael Oliver (This is true for this domain since everyone in the domain has the same first name)

False Domain: All the teenagers in the world (The statement is false for this domain because we can find so many first names from this domain)

d) Someone knows more than two other people

True Domain: All the people in the world (From all the people in the world, you can always find someone who knows more than two other people in the world)

False Domain: Everyone living alone in an island that is uninhabited (An uninhabited island means that someone lives alone there and hence he or she cannot know more than two other people since he is alone)