Question

For each sentence below, decide whether it is an atomic statement, a molecular statement, or not a statement at all.

1. There is a scary clown behind you.

2. There is a scary clown behind you and he is juggling.

3. Watch out!

Classify each of the sentences below as an atomic statement, a molecular statement, or not a statement at all. If the statement is molecular, say what kind it is (conjuction, disjunction, conditional, biconditional, negation).

1. The sum of the first 10 squares.

2. Go to your room!

3. Everybody can be fooled sometimes.

4. Every even number is divisible by 2

5. Are we human or are we dancers?

Determine whether each molecular statement below is true or false, or whether it is impossible to determine. Assume you do not know what my favorite number is (but you do know which numbers are prime).

1. If 18 is not prime, then 18 is my favorite number.

2. If 18 is my favorite number, then 18 is prime.

3. 18 is my favorite number or 3 is not my favorite number.

4. If 3 is not prime, then 3 is my favorite number.

5. If 18 is prime, then 2⋅182⋅18 is prime

6. 18 is prime or 3 is prime

In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One is a circle, and the other is a square. Each shape is drawn in a single color. Suppose you believe me when I tell you that, if the circle is green, then the square is orange. What do you therefore know about the truth value of the following statements?

1. The circle is not green or the square is orange.

2. The circle and the square are both green.

3. The circle the square are both orange.

4. If the square is orange, then the circle is green.

5. If the square is not orange, then the circle is not green.

Suppose the statement, "if the circle is red, then the square is yellow," is true. Assume also that the converse is false. Classify each statement below as true or false (if possible).

1. The circle is red.

2. The circle is red if and only if the square is not yellow.

3. The circle is red if and only if the square is yellow.

4. The square is yellow.

Consider the statement, "If you will give me magic beans, then I will give you a cow." Decide whether each statement below is the converse, the contrapositive, or neither.

1. You will give me magic beans and I will not give you a cow.

2. If you will give me magic beans, then I will not give you a cow.

3. If I will give you a cow, then you will not give me magic beans.

4. If I will give you a cow, then you will give me magic beans.

5. If you will not give me magic beans, then I will not give you a cow.

6. If I will not give you a cow, then you will not give me magic beans.

Answer 1

A statement is any declarative sentence which is either true or false. A statement is atomic if it cannot be divided into smaller statements, otherwise it is called molecular

Part1
1. There is a scary clown behind you.	atomic
2. There is a scary clown behind you and he is juggling.	molecular
3. Watch out!	not statement

Part2	result	kind
1. The sum of the first 10 squares.	not statement
2. Go to your room!	not statement
3. Everybody can be fooled sometimes.	atomic
4. Every even number is divisible by 2	atomic
5. Are we human or are we dancers?	molecular	disjunction

Part3
1. If 18 is not prime, then 18 is my favorite number.	It is impossible to tell. The hypothesis of the implication is true. Thus the implication will be true if the conclusion is true (if 18 is my favorite number) and false otherwise.
2. If 18 is my favorite number, then 18 is prime.	We cannot tell. The statement would be true if 18 is my favorite number, and false if not (since a conjunction needs both parts to be true to be true).
3. 18 is my favorite number or 3 is not my favorite number.	This is true. Either 18 is my favorite number or it is not, but whichever it is, at least one part of the disjunction is true, so the whole statement is true.
4. If 3 is not prime, then 3 is my favorite number.	This is true, again, no matter whether 3 is my favorite number or not. Any implication with a false hypothesis is true.
5. If 18 is prime, then 2⋅182⋅18 is prime	This is true, again, no matter whether 2⋅182⋅18 is prime or not. Any implication with a false hypothesis is true.
6. 18 is prime or 3 is prime	For a disjunction to be true, we just need one or the other (or both) of the parts to be true. Thus this is a true statement since 3 is prime is true statement