Convert the Pythagorean Theorem, $a^2 + b^2 = c^2$, into an implication. - "Mathematical Statements" Review Assignment - Use this assignment in your class!

"Mathematical Statements" Review Assignment

What is the difference between an atomic statement and a molecular statement?

Indicate whether or not each of the following sentences are statements:

1- The house is red.
2- Who let the dogs out?
3- Go to your room!
4- The game is on at 5 and I want to watch it.

What's are logical connectives? What are the different types of logical connectives?

$\to$ is the symbol for which logical connective?

Translate the following statement into plain English: $P \land Q \to \neg P \land \neg Q$

When is $P \lor Q$ true?

When is $P \leftrightarrow Q$ true?

In an implication $P \to Q$ , what is the hypothesis and what is the conclusion?

Convert the Pythagorean Theorem, $a^{2} + b^{2} = c^{2}$ , into an implication.

10.

What's the converse of an implication $P \to Q$ ? What's the contrapositive of an implication $P \to Q$ ?

11.

True or False: The converse of the implication "if a number greater than 2 is prime, then it is odd" is true.

12.

Rephrase the implication, "if I dream, then I am asleep" in as many different ways as possible. Then do the same for the converse.

13.

Let $P (x)$ be the predicate, " $3 x + 1$ is even." Is $P (5)$ true or false?

14.

What is a sentence called that contains variables?

15.

What types of quantifiers exist in mathematics?

16.

How can you prove $\forall x P (x)$ is false?

17.

Convert the following sentence into symbols: If a shape is a square, then it is also rectangle.

Convert the Pythagorean Theorem, $a^{2} + b^{2} = c^{2}$ , into an implication.

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Instructor solution

Alec KretchJUL 25, 2021, 10:22:10 PM

"If $a$ and $b$ are the legs of a right triangle with hypotenuse $c$ , then $a^{2} + b^{2} = c^{2}$ ."

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Discrete Mathematics (page 23)

Levin, O. (2018-12-31). Discrete Mathematics: An Open Introduction. . (Jan 26, 2024)

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True or False: $P \to Q$ implies a causal relationship between P and Q.

Select one of the following options:

A.
False
B.
True

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Convert the Pythagorean Theorem, a2+b2=c2, into an implication.

Instructor solution

Discrete Mathematics (page 23)

Think you've got it?

True or False: P→Q implies a causal relationship between P and Q.

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Convert the Pythagorean Theorem, $a^{2} + b^{2} = c^{2}$ , into an implication.

True or False: $P \to Q$ implies a causal relationship between P and Q.