LOGIC

A. Negation:______

1. What is the negation of the statement “The Sun is shining”?

1) It is cloudy.

2) It is daytime.

3) It is not raining.

4) The Sun is not shining.

2. What is the negation of the statement "Squares are parallelograms"?

1) Parallelograms are squares.

2) Parallelograms are not squares.

3) It is not the case that squares are parallelograms.

4) It is not the case that parallelograms are squares.

B. Conjunction:______

Given the following compound sentences, determine the truth-value for each.

I am a Math teacher and it is September. ______

I am a Math teacher and it is June. ______

I am a Science teacher and it is September. ______

I am a Science teacher and it is June. ______

Practice:

1. A square is round and a triangle has three sides. ______

2. Blue is a color and an apple is a fruit. ______

3. Two is even and three is odd. ______

C. Disjunction:______

Given the following compound sentences, determine the truth-value for each.

I am a Math teacher or a Science teacher. ______

I am a Math teacher or I am Mrs. Bluman. ______

I am a Science teacher or a Spanish teacher.______

I am an English teacher or a Math teacher. ______

Practice:

1. A square has 4 equal sides or a triangle has 3 sides. ______

2. Two is an even number or six is an odd number. ______

3. 5 is an odd number or 6 + 4 = 12. ______

D. Conditional Statements:______

Parts of a conditional sentence:

If it is snowing, then I will wear my boots.

Hypothesis Conclusion

Symbols: = if…then T T = T T F = F

F T = T F F = T

DETERMINING TRUTH VALUES- Given the following true statement:

If you get a 100% on your test, then your teacher will give you an A.

A.  You get a 100%; your teacher gives you an A. ______

B.  You get a 100%; your teacher gives you a B. ______

C.  You get 98%; your teacher gives you an A. ______

D.  You get 85%; your teacher gives you a B. ______

Practice:

If John gets a driver’s license, then he will buy a car.

Fact: John does not buy a car.

Which of the following statements must also be true?

(A) John gets a driver’s license.

(B) John does not get a driver’s license.

(C) John buys a car.

(D) John gets a driver’s license and buys a car

E. Bi-conditional______

Two true or two false statements make the whole statement true!!!! All other combinations are false

Example: Two intersecting segments form a right angle if and only if they are perpendicular.

Determine the truth-value of the following statements.

1.  Two is even if and only if three is odd.

2.  2 + 2 = 4 if and only if 2 + 3 = 7.

F.  Converse, Inverse, and Contrapositive

Statement / Formed by / Rule / Examples
Conditional / Given hypothesis and conclusion / If…then / If two angles have the same measure, then they are congruent.
Converse / Exchanging the hypothesis and conclusion of the conditional. / SWITCH
Inverse / Negating both the hypothesis and conclusion of the conditional. / NEGATE
Contrapositive
also called:
Logically equivalent / Negating both the hypothesis and conclusion of the converse statement. / SWITCH
AND
NEGATE