# Geometry: Logic Statements

## Problems

Problem : State the negation of the following statement:

Adrian loves rice.

Adrian does not love rice.

Problem : State the negation of the following statement:

The horse is not brown.

The horse is brown.

Problem : Given the following two statements, p and q, write their conjunction, disjunction, and the implication "if p, then q."

p: The painting is colorful
q: The painting is pretty

conjunction: The painting is colorful and the painting is pretty.
disjunction: The painting is colorful or the painting is pretty.
implication: If the painting is colorful, then the painting is pretty.

Problem : Given the following two statements, p and q, write their conjunction, disjunction, and the implication "if p, then q."

p: Two lines form a right angle.
q: Two lines are perpendicular.

conjunction: Two lines form a right angle and two lines are perpendicular.
disjunction: Two lines form a right angle or two lines are perpendicular.
implication: If two lines form a right angle, then two lines are perpendicular.

Problem : Given the following two statements, p and q, write their conjunction, disjunction, and the implication "if p, then q."

p: Frank is a doctor.
q: The birds sing.

comjunction: Frank is a doctor and the birds sing.
disjunction: Frank is a doctor or the birds sing.
implication: If Frank is a doctor, then the birds sing.