(A) Define the propositions p=“You obey the speed limit” and q=“You are going to
ID: 3667389 • Letter: #
Question
(A) Define the propositions p=“You obey the speed limit” and q=“You are going to a wedding”. Write the following sentences as compound propositions using p and q: 1. Failing to obey the speed limit implies that you are going to a wedding. 2. You drive below the speed limit only if you are going to a wedding. 3. You do not obey the speed limit unless you are going to a wedding. 4. You drive above the speed limit whenever you are going to a wedding.
(B) Define the propositions p=“The home team wins,” q=“It is raining,” r=“There is an earth- quake.” Write the following sentences as compound propositions using p, q, and r: 1. Either rain or an earthquake is sufficient for the home team to win. 2. Rain and earthquake are necessary but not sufficient for the home team to win. 3. The home team wins only if it is not raining and there is no earthquake. 4. If it is raining the home team will win unless there is an earthquake.
Explanation / Answer
~ denotes negation
A)
1. Failing to obey the speed limit implies that you are going to a wedding
ans: ~p ->q
2. You drive below the speed limit only if you are going to a wedding.
ans: q<->p
3. You do not obey the speed limit unless you are going to a wedding.
ans: ~(~p <-> q)
4. You drive above the speed limit whenever you are going to a wedding.
ans:~p <-> q
B)
1. Either rain or an earthquake is sufficient for the home team to win.
ans:(q v r) -> p
2.Rain and earthquake are necessary but not sufficient for the home team to win.
ans:(q ^ r) -> ~p
3. The home team wins only if it is not raining and there is no earthquake.
ans: ~q ^ ~ r <-> p
4. If it is raining the home team will win unless there is an earthquake.
ans: (q ^ ~r) -> p
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