Fundamentals of Logic

Open Ended

Why is understanding the fundamentals of logic important in mathematics and everyday reasoning?

Fill in the Blank

Mathematical language is used to communicate ___ and logical ideas.

Multiple Choice

Which of the following is NOT a characteristic of mathematical language?

• Precise

• Concise

• Powerful

• Ambiguous

Multiple Choice

Which words from the table are commonly associated with subtraction in mathematical problems?

• sum, add, increase

• less, minus, decrease

• multiplied, times, product

• divided, quotient, split

Fill in the Blank

Translate the phrase '3 less than twice a number".

-

Fill in the Blank

Translate the phrase “The sum of a number and 8, less 3”.

(

+

)

-

Multiple Select

Which of the following are examples of mathematical sentences?

• 3x + 4

• x + 2x = 3x

• 11m + 7

• x - 1 = 0

Multiple Choice

What is the role of the equal sign '=' in mathematical sentences?

• It acts as a mathematical verb indicating equality.

• It separates numbers from variables.

• It is used only in addition.

• It is not important in mathematical language.

Categorize

Options (16)

Cat

2

The word 'Cat' begins with the letter 'k'.

1+2=4

5-3=2

The cat is black.

x

5-3

x=1

x-1=0

t+3=3+t

x+0=x

x*1=x

t+3

This sentence is false.

Hat sat bat.

Classify the entries below as:

English Noun

Mathematical Expression

English Sentence

Mathematical Sentence

Open Ended

Explain the difference between a mathematical expression and a mathematical sentence, using examples from the slides.

Poll

1. (5-x^2) is the mathematical expression of the English phrase square of x diminished by 5.

• True

• False

Open Ended

2. Write an English phrase for a mathematical expression

   (n − 92).

Multiple Choice

3. Which of the following does not belong to the group?

• a number increased by 20

• the quotient of twenty and a number

• the product of 20 and the inverse of a number

• 20 divided by a number

Poll

4. Is 3x + 4y > 9 a mathematical sentence or just a mathematical expression?

• Mathematical Expression

• Mathematical Sentence

Poll

5. 4 − xy is the mathematical expression of the English phrase “The product of x and y subtracted from 4”.

• True

• False

Multiple Choice

Which of the following is NOT an example of a statement according to the definition in logic?

• Manila is the capital of Philippines.

• William Shakespeare wrote the television series Modern Family.

• The United States has the world’s highest divorce rate.

• What time is it?

Multiple Choice

Which of the following sentences is NOT a statement?

• If only every day could be like this one!

• The moon is made of green cheese.

• 6 is a prime number.

• February 5, 1992 falls on a Wednesday.

Multiple Choice

Statement or not?

• Statement

• Not a statement

Multiple Choice

Statement or not?

• Statement

• Not a statement

Multiple Select

Which of the following is a compound statement?

• George Washington was the first U.S. president, and John Adams was his vice president.

• If what you’ve told me is true, then we are in great peril.

• We drive across New Mexico toward the town with the curious name Truth or Consequences.

Open Ended

Let p and r represent the following component statements:

p : My backpack is heavy.

r : It’s going to rain.

Write the symbolic statement into words.

Open Ended

Let p and r represent the following component statements:

p : My backpack is heavy.

r : It’s going to rain.

Write the symbolic statement into words.

Open Ended

Let p and r represent the following component statements:

p : My backpack is heavy.

r : It’s going to rain.

Write the symbolic statement into words.

Open Ended

Let p and r represent the following component statements:

p : My backpack is heavy.

r : It’s going to rain.

Write the symbolic statement into words.

Open Ended

Let p and q represent the following component statements:

p : I pass the test.

q : I past the course.

Write the symbolic statement into words.

Open Ended

Let p and q represent the following component statements:

p : I pass the test.

q : I past the course.

Write the symbolic statement into words.

Open Ended

Let p and q represent the following component statements:

p : I pass the test.

q : I past the course.

Write the symbolic statement into words.

Open Ended

Let p, q, and r represent the following component statements:

p : A student misses lecture.

q : A student studies.

r : A student fails.

Write the symbolic statement into words.

Open Ended

Let p, q, and r represent the following component statements:

p : A student misses lecture.

q : A student studies.

r : A student fails.

Write the symbolic statement into words.

Open Ended

Let p, q, and r represent the following component statements:

p : A student misses lecture.

q : A student studies.

r : A student fails.

Write the symbolic statement into words.

Open Ended

Let p, q, and r represent the following component statements:

p : She will go on vacation.

q : She cannot take the train.

r : She cannot get a loan.

Write the symbolic statement into words.

Open Ended

Let p, q, and r represent the following component statements:

p : She will go on vacation.

q : She cannot take the train.

r : She cannot get a loan.

Write the symbolic statement into words.