Question

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 is studying discrete mathematics.
b) Everyone is older than 21 years.
c) Every two people have the same mother.
d) No two different people have the same grandmother.

Short answer

The domain for the true and false statement can be explained.

Step-by-step solution

Concept for finding domain

The domain can be found out either as true or false by converting them into logical expression. Again analyze for true and false values for the logical expression.

Finding domain as true or false for statement a)

On considering the statement and to convert the statement into logical expression. Take P(x) as the person who are all studied discrete mathematics. The statement in terms of logical expression can be written as xP(x). This logical expression is true when x is discrete mathematics students. It is false when x is the student of subject other than discrete mathematics.

Finding domain as true or false for statement b)

On considering the statement and to convert the statement into logical expression. Take P(x) as person who all older than 21 years. The statement in terms of logical expression can be written as xP(x). This logical expression is true when x is greater than 21. It is false when x is less than or equal to 21.

Finding domain as true or false for statement c)

On considering the statement and to convert the statement into logical expression. Take P(x,y) as the person having same mother. The statement in terms of logical expression can be written as P(x,y). This logical expression is true when x and y are siblings. It is false when x and y are not siblings.

Finding domain as true or false for statement d)

On considering the statement and to convert the statement into logical expression. Take P(x,y) as the person having same mother. The statement in terms of logical expression can be written as P(x,y). This logical expression is true when x and y are not siblings. It is false when x and y are siblings.