Are These Logical Negations Correct?

[charmedbeauty]

Homework Statement

Hi I just wanted to check that I'm doing these right... can someone please check the following negations.

"either the food is good and the service is excellent, or else the price is high"

negation:"The food is good or the service is excellent, and the price is low"

"Neither the food is good nor the service excellent.

negation: "either the food is good or the service is excellent"

"If the price is high, then the food is good and the service is excellent."

negation: "The price is low, and the food is good or the service is excellent"

Homework Equations

The Attempt at a Solution

above

 

[scurty]

Homework Statement

Hi I just wanted to check that I'm doing these right... can someone please check the following negations.

"either the food is good and the service is excellent, or else the price is high"

negation:"The food is good or the service is excellent, and the price is low"

"Neither the food is good nor the service excellent.

negation: "either the food is good or the service is excellent"

"If the price is high, then the food is good and the service is excellent."

negation: "The price is low, and the food is good or the service is excellent"

Homework Equations

The Attempt at a Solution

above

Sometimes it helps to write these statements in predicate logic form (it makes it simpler for me to interpret at least). If you've never seen it before, the predicate word (the word after "is") is the letter in upper case, and the subject is in the subscript. Don't worry about it if you haven't seen it before.

1) $(G_f \cdot E_s) \vee H_p$

2) $\sim (G_f \vee E_s)$

3) $H_p \supset G_f \cdot E_s$

You performed DeMorgan's Law incorrectly on the first one.

Number two looks good.

Number three doesn't look right to me, can you show your steps? (doesn't have to be in symbolic notation, it's just easier for me to see how everything changes around)

 

[charmedbeauty]

Sometimes it helps to write these statements in predicate logic form (it makes it simpler for me to interpret at least). If you've never seen it before, the predicate word (the word after "is") is the letter in upper case, and the subject is in the subscript. Don't worry about it if you haven't seen it before.

1) $(G_f \cdot E_s) \vee H_p$

2) $\sim (G_f \vee E_s)$

3) $H_p \supset G_f \cdot E_s$

You performed DeMorgan's Law incorrectly on the first one.

Number two looks good.

Number three doesn't look right to me, can you show your steps? (doesn't have to be in symbolic notation, it's just easier for me to see how everything changes around)

So when I use symbolic notation do I have to change anything or can I just simplify use equiv. laws? because I thought the negation was making a T statement F and F statement T...

But just simplifying doesn't change the outcome does it?

 

[NewtonianAlch]

I haven't done this before, but if you're negating a statement shouldn't it apply to the entire statement and not just the starting?

"If the price is high, then the food is good and the service is excellent."

negation: "The price is low, and the food is good or the service is excellent"

If high becomes low, then good food should be come bad food and excellent service should become horrible service.

I'm guessing negation is like putting a minus sign outside an equation:

-(3x^2 + 5x + 7) = -3x^2 -5x - 7I agree with scurty, the first and last one are not correct.

Also try to keep your statements in a similar manner:

If the price is high, then the food is good and the service is excellent.

Negation: If the price is ..., then the food is ... and service is ...