MGF1130 Test I Review: Mathematical Thinking & Symbolic Logic

Practice flashcards for MGF1130 Test I reviewing logical statements, symbolic representations, negations, truth tables, logical equivalences, and De Morgan's laws.

Is the sentence 'The key of C has three flats.' considered a mathematical statement?

Yes, because the sentence can be either true or false, but not both simultaneously.

Is the sentence 'Don't wait for me.' considered a mathematical statement?

No, the sentence is not a statement because it is a command.

What is the negation of the statement 'Mercury is not the closest planet to the sun.'?

Mercury is the closest planet to the sun.

Let $p$ represent 'Pigs are clean.' How is 'It is not true that pigs are clean.' written in symbolic form?

$$\sim p$$

Let $p$ be 'The job pays well' and $q$ be 'This is an octopus.' What is the symbolic form of 'The job pays well and this is an octopus.'?

$$p \land q$$

Let $p$ be 'I'm short' and $q$ be 'You're tall.' What is the symbolic form of 'You're tall, but I'm not short.'?

$$q \land \sim p$$

Let $p$ be 'It is Sunday' and $q$ be 'The office is closed.' What is the symbolic form of 'The office is not closed if and only if it is not Sunday.'?

$$\sim q \leftrightarrow \sim p$$

Let $p$ be 'The campus is closed' and $q$ be 'It is Sunday.' What is the symbolic form of 'The campus is not closed if and only if it is not Sunday.'?

$$\sim p \leftrightarrow \sim q$$

Given $p: 4+2=5$ and $q: 5 \times 3 = 30$, what is the truth value of the statement $p \lor \sim q$?

$p \lor \sim q$ is true.

For the statement $p: 3+4=6$, what is the truth value of $p \lor \sim p$?

$p \lor \sim p$ is true.

What are the truth values for the biconditional negation statement $\sim(p \leftrightarrow q)$ for truth combinations TT, TF, FT, and FF?

False for TT, True for TF, True for FT, and False for FF.

Are the statements $(r \land q) \land p$ and $r \land (q \land p)$ logically equivalent?

Yes, the statements are equivalent.

What is the negation of the conditional statement 'If I am in Albany, then I am in New York.'?

I am in Albany and I am not in New York.

What is the negation of the conditional statement 'If the fish does not have scales, then the cat has fur.'?

The fish does not have scales and the cat does not have fur.

Using De Morgan's laws, what is an equivalent form of 'It is not true that dust and hair are both found on the furniture.'?

Dust is not found on the furniture or hair is not found on the furniture.