IM1 Review Ch 9: Logic

Write the following in "If-then form".

Two lines intersect in a point.

• If two lines make a point, then they intersect.

• If two lines intersect, then it is a point.

• If there is a point, then two lines intersect.

Write the following in "If-then form".

Two angles add up to 180^o if they are supplementary.

• If two angles add up to 180^o, then they are supplementary.

• If two angles are supplementary, then they add up to 180^o_.

Write the CONVERSE of the conditional statement:

If an angle is a right angle, then it measures 90^o.

• If an angle measures 90^o, then it is a right angle.

• If an angle is not a right angle, then it does not measures 90^o.

• If an angle does not measure 90^o, then it is not a right angle.

• An angle is a right angle if and only if it measures 90^o.

Write the CONTAPOSITIVE of the conditional statement:

If an angle is a right angle, then it measures 90^o.

• If an angle measures 90^o, then it is a right angle.

• If an angle is not a right angle, then it does not measures 90^o.

• If an angle does not measure 90^o, then it is not a right angle.

• An angle is a right angle if and only if it measures 90^o.

Write the INVERSE of the conditional statement:

If you don't like dogs, then you wouldn't get one.

• If you like dogs, then you would get one.

• If you wouldn't get a dog, then you don't like them.

• If you would get a dog, then you like them.

• You don't like dogs if and only if you wouldn't get one.

Write the BICONDITIONAL STATEMENT:

If you don't like dogs, then you wouldn't get one.

• If you like dogs, then you would get one.

• If you wouldn't get a dog, then you don't like them.

• If you would get a dog, then you like them.

• You don't like dogs if and only if you wouldn't get one.

Find the "If-then Form" of the statement 4x + 9 = 21 so x = 3. Then find the inverse, converse, contraposiive, and biconditional statement.

• If 4x + 9 = 21,

  then x = 3.

• Contrapositive

• If x = 3,

  then 4x + 9 = 21.

• "If-then Form"

• If 4x + 9 ≠ 21, then x ≠ 3.

• Converse

• 4x + 9 = 21 if and only if x = 3.

• Inverse

• If 4x + 9 ≠ 21,

  then x ≠ 3.

• Biconditional Statement

Find the "If-then Form" of the statement "I do math if I'm bored." Then find the inverse, converse, contraposiive, and biconditional statement.

• If I don't do math, then I'm not bored.

• Contrapositive

• If I'm bored, then I do math.

• "If-then Form"

• If I do math, then I'm bored.

• Converse

• If I'm not bored, then I don't do math.

• Inverse

Inductive reasoning is when you come to a conclusion based on:

• Definition

• Fact

• Observation

Which of the following is an example of inductive reasoning?

• A right angle measures 90^o. Since angle 1 is a right angle, it is 90^o.

• Every Friday, your friend comes over. It is Friday, so they will come over.