# HW 6.3, part III, #10

## Re: 6.3 III #10 more examples

Here is another example:

# 9

“Cindy, Jane, and Amanda witnessed a bank robbery. At trial, Cindy testified that Lefty did not enter the back, and if Howard pulled a gun, then Conrad collected the money. Jane testified that if Howard did not pull a gun, then Lefty entered the bank. Amanda testified that if Conrad collected the money, then Howard pulled a gun. Is it possible that all three witnesses told the truth? If so, what can we conclude about Lefty, Howard, and Conrad?”

Hurley is asking if these four statements are consistent with each other. Can they all be true at the same time? If so, then under what conditions?

2. Translate them into symbols:

Cindy: “Lefty did not enter the back.” ~ L

“If Howard pulled a gun, then Conrad collected the money.” H -> C

Jane “If Howard did not pull a gun, then Lefty entered the bank.” ~ H -> L

Amanda “If Conrad collected the money, then Howard pulled a gun.” C -> H

3. Make a truth table

L H C / ~ L / H -> C / ~ H -> L / C -> H

1. T T T F T T T

2. T T F F F T T

3. T F T F T T F

4. T F F F T T T

5. F T T T T T T

6. F T F T F T T

7. F F T T T F F

8. F F F T T F T

2. Evaluate the truth table

These three witness statements are consistent. So it is possible that everyone is telling truth. If so, then ~L, H, and C (see row five). So, Lefty did not enter the bank, Howard pulled the gun, and Conrad collected the money.

# 9

“Cindy, Jane, and Amanda witnessed a bank robbery. At trial, Cindy testified that Lefty did not enter the back, and if Howard pulled a gun, then Conrad collected the money. Jane testified that if Howard did not pull a gun, then Lefty entered the bank. Amanda testified that if Conrad collected the money, then Howard pulled a gun. Is it possible that all three witnesses told the truth? If so, what can we conclude about Lefty, Howard, and Conrad?”

Hurley is asking if these four statements are consistent with each other. Can they all be true at the same time? If so, then under what conditions?

2. Translate them into symbols:

Cindy: “Lefty did not enter the back.” ~ L

“If Howard pulled a gun, then Conrad collected the money.” H -> C

Jane “If Howard did not pull a gun, then Lefty entered the bank.” ~ H -> L

Amanda “If Conrad collected the money, then Howard pulled a gun.” C -> H

3. Make a truth table

L H C / ~ L / H -> C / ~ H -> L / C -> H

1. T T T F T T T

2. T T F F F T T

3. T F T F T T F

4. T F F F T T T

5. F T T T T T T

6. F T F T F T T

7. F F T T T F F

8. F F F T T F T

2. Evaluate the truth table

These three witness statements are consistent. So it is possible that everyone is telling truth. If so, then ~L, H, and C (see row five). So, Lefty did not enter the bank, Howard pulled the gun, and Conrad collected the money.

**Monica**- Guest

## Re: 6.3 III #10

6.3 III.

Okay, so to do these problems, first translate the sentences into symbolic language. For #10, there are four statements. Hurley is asking if they are consistent with each other. Can they all be true at the same time? If so, then under what conditions?

For examples, let's look at the other problems in III:

#3.

“Christina and Thomas are having a discussion about their plans for the evening. Christina: “If you don’t love me, then I’m certainly not going to have sex with you.” Thomas: “Well, that means that if you do love me, then you will have sex with me, right?” Is Thomas correct” (Hint: Construct a truth table for each statement and compare them).

So this questions is asking if the two statements are logically equivalent.

1. Translate them into symbols:

“If you don’t love me, then I’m certainly not going to have sex with you.”

~ L -> ~ S

“If you do love me, then you will have sex with me.”

L -> S

2. Make a truth table

L S / ~L -> ~ S / L -> S

T T T T

T F T F

F T F T

F F T T

3. Evaluate the truth table

Thomas is not correct. These statements are not logically equivalent (they don’t mean the same thing). Christina said that being in love is a necessary condition for having sex. However, Thomas mistakenly interpreted her as saying that being in love is a sufficient condition for having sex. (The statements are consistent, though. Christina hasn’t ruled out L->S; she just hasn’t agreed to it.)

Okay, so to do these problems, first translate the sentences into symbolic language. For #10, there are four statements. Hurley is asking if they are consistent with each other. Can they all be true at the same time? If so, then under what conditions?

For examples, let's look at the other problems in III:

#3.

“Christina and Thomas are having a discussion about their plans for the evening. Christina: “If you don’t love me, then I’m certainly not going to have sex with you.” Thomas: “Well, that means that if you do love me, then you will have sex with me, right?” Is Thomas correct” (Hint: Construct a truth table for each statement and compare them).

So this questions is asking if the two statements are logically equivalent.

1. Translate them into symbols:

“If you don’t love me, then I’m certainly not going to have sex with you.”

~ L -> ~ S

“If you do love me, then you will have sex with me.”

L -> S

2. Make a truth table

L S / ~L -> ~ S / L -> S

T T T T

T F T F

F T F T

F F T T

3. Evaluate the truth table

Thomas is not correct. These statements are not logically equivalent (they don’t mean the same thing). Christina said that being in love is a necessary condition for having sex. However, Thomas mistakenly interpreted her as saying that being in love is a sufficient condition for having sex. (The statements are consistent, though. Christina hasn’t ruled out L->S; she just hasn’t agreed to it.)

**Monica**- Guest

## HW 6.3, part III, #10

Hi. I'm having some trouble with getting this one started. I don't know how many parts to break it up into to do the truth table. Is is all one piece or two or three different ones? I hope this makes sense. Any help is appreciated!

**Paige**- Guest

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