Review for Test Chapter 3

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.

All chocolate is good.

• If itʹs chocolate, then itʹs good.

• If itʹs good, then itʹs got to be chocolate.

• If it isnʹt chocolate, then it isnʹt good.

• Chocolate is good.

Write the converse, inverse, or contrapositive of the statement as requested.

All cats catch birds.

Inverse

• If itʹs not a cat, it doesnʹt catch birds.

• Not all cats catch birds.

• If it doesnʹt catch birds, itʹs not a cat.

• If it catches birds, itʹs a cat.

Tell whether the conditional statement is true or false.

(5 = 5) → (4 = 3)

• True

• False

Rewrite the statement in the form ʺif p, then qʺ.

I will be happy only if he calls.

• If I am happy, then he must have called.

• If he calls, then I will be happy.

• If I am not happy, then he will call.

• If I am happy, then he wonʹt call.

Let p represent 7 < 8, q represent 2 < 5 < 6, and r represent 3 < 2. Decide whether the statement is true or false

~q ∧ ~r

• True

• False

Write the compound statement in words.

Let r = ʺThe puppy is trained.ʺ

p = ʺThe puppy behaves well.ʺ

q = ʺHis owners are happy.ʺ

p → r

• If the puppy behaves well then the puppy is trained.

• The puppy behaves well or the puppy is trained.

• The puppy does not behave well or the puppy is not trained.

• If the puppy is trained then the puppy behaves well.

Find the truth value of the statement.

9 - 4 = 5 if and only if 9 + 3 = 13.

• True

• False

p represents the statement ʺHer name is Lisa.ʺ

q represents the statement ʺShe lives in Chicago.ʺ

Translate the following compound statement into words:

p ∧ q

• Her name is Lisa and she lives in Chicago.

• Her name is Lisa or she lives in Chicago.

• Her name is Lisa and she doesnʹt live in Chicago.

• If her name is Lisa, she lives in Chicago.

Give the number of rows in the truth table for the compound statement.

p ∨ (~q ∨ r)

• 8

• 6

• 3

• 9

Write the compound statement in symbols.

Let r = ʺThe food is good.ʺ

p = ʺI eat too much.ʺ

q = ʺIʹll exercise.ʺ

If I exercise, then I wonʹt eat too much.

• q → ~p

• ~(p → q)

• r ∧p

• p → q