Exam 2: Introduction to Logic and Sets

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form. -If the food is good and if I eat too much, then I'll exercise.

Rewrite the statement using mathematical symbols. -The set A is the set containing only the element 6.

Write in if-then form. - $x = 8$ only if $2 x + 3 = 19$ .

Determine the validity of the argument. -Martians are green. Roger is not green. Therefore Roger is not a Martian.

Write the set as indicated. -Write $\{ 17,18,19,20 \}$ using set-builder notation.

Write a valid conclusion based on the statements. -If it's not Saturday, then Dad will shave. If Dad has whiskers, then he did not shave. If it's Saturday, then Dad will take us to the game.

Is it possible or not possible to set up a one-to-one correspondence between {0, 6, 9, 19} and {6, 9, 19}?

Write in if-then form. -An even number is divisible by two.

Use a quantifier to make the following true or false, as indicated, where x is a natural number. - $4 \mathrm { x } = 7 \mathrm { x }$ (make false)

Provide an appropriate response. -A is the set of all even natural numbers, and B is the set of all odd natural numbers. Describe a universal set for A and B. Also, with respect to this universal set, give a relationship between A and B.

Write a valid conclusion based on the statements. -Hard workers sweat. Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold.

Rewrite the statement using mathematical symbols. -The set consisting of the elements $k$ and $z$ is not a proper subset of $\{ c , f , z , u \}$ .

Provide an appropriate response. -Determine the validity of the following conclusion and explain: If you walk fast, then you will reach the bus stop on time. If you reach the bus stop on time, then you will catch the bus. If you walk fast, then you will catch the bus.

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form. -If I eat too much, then I'll exercise.

Construct a truth table for the statement. - $\sim((w \wedge \mathrm{q}) \vee \mathrm{S})$

Determine the validity of the argument. -Some investments are risky. Real estate is an investment. Therefore real estate is risky.

Rewrite the statement using mathematical symbols. -P is the set of even numbers less than 30 and more than 20.

Find n(A)for the set A. -A = {3, 5, 7, 9, 11}

Write a valid conclusion based on the statements. -Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form. -I'll exercise if I eat too much.