Unit 2: Sections 2-1 to 2-4

Question 1

Conditional Statement?

Answer 1

A statement that is written in the If-then form.

Question 2

Hypothesis?

Answer 2

The “if” part of a conditional statement.

Question 3

Conclusion?

Answer 3

The “then” part of a conditional statement.

Question 4

Counterexample?

Answer 4

An example that shows that a conditional statement is false.

Question 5

Converse?

Answer 5

Interchanging the hypothesis and conclusion.

Question 6

Symbol for not?

Answer 6

~ (called the tilde)

Question 7

Symbol for conjunction?

Answer 7

^ (to express the word and)

Question 8

Symbol for or?

Answer 8

V (to express the word or)

Question 9

Biconditional?

Answer 9

When both a conditional and its converse are true.
Indicated by iff.
There can be false biconditionals.
A good definition is always a good biconditional.

Question 10

Inverse?

Answer 10

Both the hypothesis and the conclusion are negated (turned negative) using the word not.

Question 11

Contrapositive?

Answer 11

When the hypothesis and conclusion are negated and interchanged.

Question 12

The Law of Detachment?

Answer 12

If a conditional is true and the hypothesis is true then the conclusion is true.

Question 13

The Law of Syllogism?

Answer 13

If p → q and q → r are true statements then
p → r is a true statement.

Question 14

Reflexive Property of Equality?

Answer 14

a = a.

Question 15

Symmetric Property of Equality?

Answer 15

If a = b, then b = a.

Question 16

Transitive Property of Equality?

Answer 16

If a = b, and b = c, then a = c.

Question 17

Addition Property of Equality?

Answer 17

If a = b, then a + c = b + c.

Question 18

Subtraction Property of Equality?

Answer 18

If a = b, then a - c = b - c.

Question 19

Multiplication Property of Equality?

Answer 19

If a = b, then ac = bc.

Question 20

Division Property of Equality?

Answer 20

If a = b, and c ≠ 0, then, a/c = b/c.

Question 21

Substitution Property of Equality?

Answer 21

If a = b, then a and b may be substituted each other in any equation or inequality.

Question 22

Addition Commutive Property of Real numbers?

Answer 22

a + b = b + a

Question 23

Multiplication Commutive Property of Real numbers?

Answer 23

ab = ba

Question 24

Associative Property of Real numbers?

Answer 24

a + (b + c) = (a + b) + c
a * (b * c) = (a * b) * c

Question 25

Distributive Property of Real numbers?

Answer 25

a(b + c) = ab +ac

Question 26

Reflexive Property of Congruence?

Answer 26

<A ≅ <A

Question 27

Symmetric Property of Congruence?

Answer 27

If <A ≅ <B, then <B ≅ <A

Question 28

Transitive Property of Congruence?

Answer 28

If <A ≅ < B, and <B ≅ <C, then <A ≅ <C