Logic Review

How is statement B related to statement A?

Statement A: "Two perpendicular lines always form a right angle."

Statement B: "If two lines are perpendicular, then they form a right angle."

• conditional

• converse

• inverse

• contrapositive

• biconditional

Answer explanation

conditional is writing a statement in if-then form

How is statement B related to statement A?

Statement A: If two lines are perpendicular, then they form a right angle.

Statement B: If two lines form a right angle, then they are perpendicular.

• conditional

• converse

• inverse

• contrapositive

• biconditional

Answer explanation

converse is the reverse of a conditional

switch the hypothesis and conclusion of the statement

How is statement B related to statement A?

Statement A: If two lines are perpendicular, then they form a right angle.

Statement B: If two lines are not perpendicular, then they do not form a right angle.

• conditional

• converse

• inverse

• contrapositive

• biconditional

Answer explanation

inverse is the negation of the hypothesis and conclusion of a statement

How is statement B related to statement A?

Statement A: If two lines are perpendicular, then they form a right angle.

Statement B: If two lines do not form a right angle, then they are not perpendicular.

• conditional

• converse

• inverse

• contrapositive

• biconditional

Answer explanation

contrapositive is the switching and negating of the hypothesis and conclusion

Write the following statement as a biconditional.

Statement: If two lines are perpendicular, then they form a right angle.

• If two lines form a right angle, then they are perpendicular.

• Two lines are perpendicular if and only if they form a right angle.

• Two lines form a right angle if and only if they are perpendicular.

• If two lines do not form a right angle, then they are not perpendicular.

• Two lines are not perpendicular if and only if they do not form a right angle.

Answer explanation

biconditional is p if and only if q.

Tags

CCSS.HSG.CO.C.9

Let p = An equation is of the form y = mx + b.

Let q = Its graph is a line.

Argument:

If an equation is of the form y = mx + b, then its graph is a line.

The graph is not a line.

Therefore, the equation is not the form of y = mx + b.

Which of the following is the symbolic representation of the given argument?

• 
• 
• 
• 

Tags

CCSS.HSS.CP.B.7

Assume the following statements are true.

If Ali wears a green shirt, then we will take a test.

If we take a test, then everyone will pass the test.

Determine the conclusion and what law was used.

• If everyone passes the test, then Ali wore a green shirt.

  Law of Syllogism

• Everyone will not pass the test.

  Law of Contrapositive

• Everyone will pass the test.

  Law of Detachment

• If Ali wears a green shirt, then everyone will pass the test.

  Law of Syllogism

Answer explanation

What is a valid counterexample for the following conjecture.

"The square root of a number x is always less than x."

• 1

• -1

• 81

• 9

Answer explanation

Counterexample is an example that proves the statement is false in which the hypothesis is true but the conclusion is false
$\sqrt{1}$ =1 so it is not less than 1
$\sqrt{-1}$ is an imaginary number
$\sqrt{81}$ is less than 81
$\sqrt{9}$ is less than 9