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"Mathematical Statements" Review Assignment

*1.*What is the difference between an atomic statement and a molecular statement?*2.*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.*3.*What's are logical connectives? What are the different types of logical connectives?*4.*\(\rightarrow\) is the symbol for which logical connective?*5.*Translate the following statement into plain English: \(P \land Q \rightarrow \lnot P \land \lnot Q\)*6.*When is \(P \lor Q\) true?*7.*When is \(P \leftrightarrow Q\) true?*8.*In an implication \(P \rightarrow Q\), what is the hypothesis and what is the conclusion?*9.*Convert the Pythagorean Theorem, \(a^2 + b^2 = c^2\), into an implication.*10.*What's the converse of an implication \(P \rightarrow Q\)? What's the contrapositive of an implication \(P \rightarrow Q\)?*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, "\(3x + 1\) 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.

Levin, O. (2018-12-31). Discrete Mathematics: An Open Introduction. . (Feb 5, 2023)

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