G.1b Symbolic Form

Let p represent

All rectangles are parallelograms.

and let q represent

Some rectangles are not squares.

Which is a representation of the statement below?

All rectangles are parallelograms or some rectangles are squares.

• p Λ ∼q

• ∼p Λ q

• p ∨ ∼q

• ∼p ∨ q

Consider the following statements.

p: two lines are parallel

q: corresponding angles are congruent

Which of the following is the symbolic representation of the statement,

If two lines are not parallel, then corresponding angles are not congruent.

• ∼p→∼q

• ∼q→∼p

• q→p

• p→q

Let p represent “x² ≠ 64.”

Let q represent “x is not a rational number.” Which is a representation of the statement below?

If x is a rational number, then x² = 64.

• ∼p→∼q

• ∼p→q

• p→∼q

• ∼q→∼p

Let p represent

∠A is acute.

Let q represent

∠B is acute.

Create a symbolic representation of the following argument.

• p→q

• p↔q

• p∧q

• p⋎q

• ∴p∧q

Consider the following statements represented by pand q:

p: The sum of two angles is 180°.

q: The two angles are supplements.

Which of the following is a symbolic representation of the statement

"If two angles are not supplements, then the sum of the two angles is not 180°."

• q→∼p

• p→∼q

• ∼q→∼p

• ∼p→∼q

Let r represent: Angle A is a right angle.

Let s represent: Angle B is a right angle.

Which is a symbolic representation of the following argument?

Angle A is a right angle if and only if Angle B is a right angle.

Angle A is a right angle or Angle B is a right angle.

Therefore Angle A is a right angle and Angle B is a right angle.

• r↔s

  r∨s

  ∴r∧s

• r→s

  r∧s

  ∴r∨s

• r↔s

  r∧s

  ∴r∨s

• r→s

  r∨s

  ∴r∧s

Let s represent “eat your vegetables,” let r represent “eat your dessert,” and t represent “you can go to the party.” Which statement represents ∼r→t?

• If you eat your vegetables, then you can go to the party.

• If you eat your dessert, then you can to the party.

• If you do not eat your vegetables, then you cannot go the party.

• If you do not eat your dessert, then you can go to the party.

Let p represent “Figures are squares,” let q represent “Figures are rectangles,” and let r represent “Figures are rhombi.” Which statements represent the following argument?

• All squares are rectangles.

  ABCD is a square.

  Therefore, ABCD is a rectangle.

• If a figure is a square, then it is a rhombus.

  A figure is a rhombus.

  Therefore, a figure is a square.

• All squares are rhombi.

  ABCD is a square.

  Therefore, ABCD is a rhombus.

• If a square is a rectangle, then it is a rhombus.

  A square is a rectangle.

  Therefore, a square is a rhombus.

Let p represent: Brent works this summer.
Let q represent: Brent takes a vacation.
What is the symbolic representation of this statement?
Therefore, Brent does not work this summer.

• ∴~p
• ∴~q
• ~p
• ~q

Let p represent "Daniel is angry", and let q represent "Daniel is not having fun."
Translate the following into symbolic form...
Daniel is angry and Daniel is not having fun.

• p ^ q
• q ^ p
• ~p ^ ~q
• ~q ^ ~p