Lecture 2 Symbolic Logic Worksheet With Answers printable pdf download

Lecture 2 Symbolic Logic Worksheet With Answers

Lecture 2, Symbolic Logic

Statement: A statement is a sentence that is either true or false

Example 1: Which of the following are statements? Why or why not?

a. Apple manufactures computers.

b. Apple manufactures the world’s best computers.

c. Did you buy an IBM?

d. A $2,000 computer that is discounted 25% will cost $1,000.

e. I am telling a lie.

Solution:

a. Yes

b. No. It is true for some people and false for others. Therefore, it is not a statement.

c. No. It is a question

d. Yes. But it is a false statement

e. No. It is a paradox. (A paradox is a sentence that contradicts itself.)

If it were true, the speaker would be telling a lie, but in telling the truth, the

speaker would be contradicting the statement that he or she was lying;

If it were false, the speaker would not be telling a lie, but in not telling a lie, the

speaker would be contradicting the statement that he or she was lying.

A compound statement is a statement that contains one or more simpler statements.

Example: Charles donated blood and did not wash his car.

Negation: The negation of a statement “p” is the denial of the statement and is

represented by the symbol “~p”.

Example 2: Write a sentence that represents the negation of each statement:

a. The senator is a Democrat

b. The senator is not a Democrat.

c. Some senators are Republicans.

d. All senators are Republicans.

e. No senator is a Republican.

Solution: (1) “a” and “b” are negations of each other.

(2) “c” and “e” are negations of each other.

(3) For “d”, the negation is “Some senators are not Republicans”

Note: For question “c”, “d” and “e”, we would like to use the Venn diagram too.

All p are q.

No p are q.

Some p are q.

Some p are not q.

Lecture 2 Symbolic Logic Worksheet With Answers