Discrete Mathematics (page 30)
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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.