1) Let p and q be the propositions p: You drive over 65 miles per hour. q: You g

Question

1) Let p and q be the propositions
p: You drive over 65 miles per hour.
q: You get a speeding ticket.
Write each of the following propositions using p and q and logical connectives.
1. You do not drive over 65 miles per hour.
2. You drive over 65 miles per hour, but you do not get a speeding ticket.
3. You will get a speeding ticket if you drive over 65 miles per hour.
4. If you do not drive over 65 miles per hour, then you will not get a speeding ticket.
5. Driving over 65 miles per hour is sufficient for getting a speeding ticket.
6. You get a speeding ticket, but you do not drive over 65 miles per hour.
7. Whenever you get a speeding ticket, you are driving over 65 miles per hour.

2)Write each of the following propositions in the form

Explanation / Answer

1)

1. You do not drive over 65 miles per hour.== ~p
2. You drive over 65 miles per hour, but you do not get a speeding ticket.== (p ^ ~q)
3. You will get a speeding ticket if you drive over 65 miles per hour.== (p -->q)
4. If you do not drive over 65 miles per hour, then you will not get a speeding ticket. (~p -->~q)
5. Driving over 65 miles per hour is sufficient for getting a speeding ticket.   (p=>q)
6. You get a speeding ticket, but you do not drive over 65 miles per hour.         (q ^ ~p)
7. Whenever you get a speeding ticket, you are driving over 65 miles per hour.        (q => p)

2)1. I will remember to send you the address only if you send me an e-mail message.

if you send me an e-mail message then I will remember to send you the address

2. To be a citizen of this country, it is sufficient that you were born in the Unites

If you were born in the Unites then u can be citizen of this country

3)

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