Geometry SOL G.1 Logic #1

Given the statements:

If a shape is a parallelogram, then it's consecutive angles are supplementary.

A square is a parallelogram.

Which is a logical conclusion from the given statement?

• The consecutive sides of a square supplementary.

• The opposite angles of a square are supplementary.

• A square is a quadrilateral.

• The consecutive angles of a square are supplementary.

Tags

CCSS.HSG.CO.C.11

Which is the contrapositive of the following statement?

If ^x∕_y=z, then x=zy.

• If x = zy, then ^x∕_y = z.

• If ^x∕_y ≠ z, then x ≠ zy.

• If x ≠ zy, then ^x∕_y ≠ z.

• If x = zy, then ^x∕_y ≠ z.

Let p represent; Sam gets a job.

Let q represent; Sam will be available after school.

Which symbolically represents the following argument;

If sam gets a job, then he won't be available after school.

Sam is available after school.

Therefore, Sam did not get a job.

• p-> ~q

  q

  ∴~p

• p-> q

  ~q

  ∴~p

• q-> p

  ~q

  ∧~p

• p-> ~q

  ~q

  ∨~p

Given the statement;

If an angle is right, then it has an angle measure of 90°

<ABC is a right angle.

Which is a valid conclusion?

• <ABC is a right angle.

• <ABC is an angle in a square.

• <ABC has a measure of 90°

• There is not enough information

Let p represent: Two angles are supplementary.

Let q represent: The angles have a sum of 180°

What is the symbolic representation of the following statement;

If two angles have a sum of 180°, then the angles are supplementary.

• p -> q

• q -> p

• ~p -> q

• ~q -> ~p

What is the converse of the following statement?

If the figure was dilated with a scale factor greater than one, then the figure was enlarged.

• If the figure was not dilated with a scale factor greater then on, then the figure was not enlarged.

• If the figure was enlarged, then the figure was dilated with a scale factor greater then 1.

• If the figure was not enlarged, then the figure was dilated with a scale factor less then one.

• If the figure was enlarged, then the figure was dilated with a scale factor less than one.

Tags

CCSS.HSG.SRT.A.1

Given the following statements, which is a valid conclusion;

If the Blue Socks beat the Green Socks, then they will go to the championship game. If they go to the championship game, then they will play the Orange Socks.

• If the Green Socks go the the championship game, then the Blue Socks will play the Orange Socks.

• If the Orange Socks go to the championship game, then the Blue socks will beat the Green Socks.

• If the Blue Socks don't beat the Green Socks, then the Green Socks will play the Orange Socks.

• If the Blue Socks beat the Green Socks, then they will play the Orange Socks.

What is the inverse of the following statement;

If a pair of alternate interior angles are congruent, then the lines are parallel.

• If the lines are not parallel then a pair of alternate interior angles are congruent.

• If a pair of alternate interior angles are not congruent, then the lines are not parallel.

• If a pair of alternate interior angles are not congruent, then the lines are parallel

• If the lines are parallel, then a pair of alternate interior angles are congruent.

Tags

CCSS.HSG.CO.C.9

Let p represent John passes his SOL.

Let q represent John graduates.

Let r represent John goes to summer school

Symbolically represent the following;

If John passes his SOL, then he graduates.

If John graduates, then he doesn't go to summer school.

John passes his SOL

Therefore John doesn't go to summer school.

• p -> q

  q -> ~r

  p

  ∴~r

• p -> q

  q -> ~r

  p

  ∴r

• p -> ~q

  ~q -> r

  p

  ∴~r

Tags

CCSS.HSS.CP.A.1

What is the inverse of the following statement?

If Sam buys a car then he does not buy a motorcycle.

• If Sam doesn't buy a car the he buys a motorcycle.

• If Sam doesn't buy a car the he doesn't buys a motorcycle.

• If Sam buys a motorcycle then he doesn't buy a car the he

• If Sam doesn't buy a motorcycle, then he buys a car.

Tags

CCSS.HSS.CP.A.1