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

"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.

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Instructor solution

Alec KretchAUG 12, 2021, 8:24:34 AM

An atomic statement cannot be broken down into multiple, smaller statements.

A molecular statement can be broken down into multiple, smaller statements.

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Discrete Mathematics (pages 20, 21)

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

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Select the molecular statement from the following options:

Select one of the following options:

A.
My name is Alec and I'm a software engineer.
B.
$5 \times 3 = 15$
C.
1+x=3
D.
The largest state in the U.S. is Arkansas.

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