Question

Use the mathematical expression ‘ x ’ in three sentences: one that is always true, one
that is always false, and whose truth cannot be determined without additional information.

Answer 1

Answer:

for a real number x

true: x² is a real number

false: x² is an imaginary number

cannot be determined: x² is 4 (it cannot be determined till we are given info about whether x=2 or not)

Answer 2

Answer:

The first statement is always true.

Let 'x' be Sun.

• The statement can be: 'x is a star.'
• Sun is a star, this is always a true statement.

The second statement is always false.

Let 'x' be Sun.

• The statement can be: 'x is a planet.'
• Sun is a star and not a planet, hence this is always a false statement.

The third statement cannot be determined without additional information.

Let 'x' be Sun.

• The statement can be: 'x has helium present in it.'
• Sun is a star, but we cannot predict its chemical composition until some data is provided.