Logical Reasoning

Which is the converse of:
"If a figure is a circle with radius r, then its circumference in 2(pi)r."

• If a figure has a circumference of 2(pi)r, then its a circle with radius r.
• If a figure doesn't have a circumference, then it's a circle with a radius of r.
• If a figure isn't a circle with radius r, then its circumference isn't 2(pi)r
• If a figure isn't a circle, then it doesn't have a circumference.

Contrapositive of:
If an integer ends with 0, then it's divisible by 2.

• If an integer ends with 2 then it's divisible by 0.
• If an integer doesn't end in 0, then it's not divisible by 2.
• If an integer isn't divisible by 2, then it's doesn't end in 0.
• If an integer is divisible by 2, then it ends with 0.

Inverse of: 
If you win the championship game, then you win the league trophy.

• If you don't win the championship game, then you don't win the league trophy.
• If you win the league trophy, then you win the championship game.
• If you don't win the league trophy, then you don't win the championship game.
• If you don't play the game, you can't win a trophy.

Which statement is a good definition of a rectangle?

• A rectangle is a shape with four sides.
• A rectangle is a shape with two pairs of parallel sides.
• A rectangle is a quadrilateral with four congruent angles.
• A rectangle is a parallelogram with four congruent sides.

Conditional:  If a triangle is scalene, then it has no congruent sides. 
Which statement shows the conditional written as a true biconditional?

• A triangle is scalene if and only if it has no congruent sides.
• If a triangle has no congruent sides, then the triangle is scalene.
• If a triangle has some congruent sides, then the tringle is not scalene.
• A triangle is equilateral if and only if it is not scalene.

Which of the following is a good definition?

• grass is green.
• A yard is a unit of measure exactly 3 ft long.
• Dinosaurs are extinct.
• A pound weighs more than an ounce.

Which conclusion can you make?
If a whole number ends in 0, then it is divisible by 10. 
If a whole number is divisible by 10, then it is divisible by 5.

• If a whole number ends in 10 then it's divisible by 0.
• If a whole number ends in 5, then it's divisible by 10.
• If a whole number ends in 0, then it's divisible by 5.
• No conclusion can be made.

Which statement is a valid conclusion based on the argument?
If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.
The polygon is a regular pentagon.

• The polygon is a rectangle.
• The polygon is a regular quadrilateral.
• The polygon has exactly five congruent angles.
• The polygon has congruent sides.

Which of the following completes the statement to form a valid conclusion? 
If it is snowing heavily, then school will be canceled. 
If school is canceled, the big test will not be given today.
It is snowing heavily, therefore...

• look out for the snowplows while driving to school.
• the big test will not be given today.
• the roads will be hard to drive on.
• you should call the school to see if school is canceled.

Which statement is a valid conclusion?
If a student has a temperature of 100 or more, then he/she should stay home from school. 
Jake has a temperature of 101 and Suzi has a temperature of 99.

• Both Jake and Suzi should stay home.
• Both should go see the school nurse.
• Jake should stay home, but Suzi should go to school.
• Suzi should stay home, but Jake should go to school.