PE 1.4

Choose whether the following statements are consistent or inconsistent Yojimbo js talked than Sanjuro. Yojimbo is shorter than Maguro Maguro is shorter than Sanjuro.

Inconsistent

There are ten cows in the pasture. There are hundreds of cows in the pasture. The above statements

The second implies the first but not vice versa

All students work hard. No students work hard. The above statements

Can't both be true but can both be false

Choose whether the following statements are consistent or inconsistent Nicky is the best chess player in the class Nicky is the worst chess player in the class

Consistent

Choose whether the following statements are consistent or inconsistent If you leave me, I'll kill myself If you leave me, I'll have another martini

Consistent.

Choose whether the following statements are equivalent or non-equivalent We are not both going to the game and the concert. Either we are not going to the game or we are not going to the concert.

Equivalent

All students are hard workers. Some students are not hard workers. The above statements

Can't both be false and can't both be true

He either went to Stanford or Berkeley. He neither went to Stanford nor Berkeley. The above statements

Can't both be false and can't both be true

If he went to France then he saw Paris. He went to France and did not see Paris. The above statements

Can't both be false and can't both be true

It's a snake and it's poisonous. It's neither a snake nor poisonous. The above statements

Can't both be true but can both be false

Choose whether the following statements are consistent or inconsistent Melville is not very clever. Melville is a college professor.

Consistent. A person who is not very clever is not logically excluded from being a college professor. Hence, these statements can both be true. They are consistent.

Choose whether the following statements are equivalent or non-equivalent We are not going either to the game or the concert. We are not going to the game and we are not going to the concert. We are going neither to the game nor the concert

Equivalent.

If extra terrestrials visit earth, they will be highly civilized. If the above statement is true, then which of the following cannot be true?

Extra terrestrials visit earth and they are not highly civilized

A statement P implies a statement Q if and only if whenever Q is true, then P is true

False

Two statements are contraries if and only if they cannot both be true and cannot be false given the same circumstances.

False. Contraries cant both be true, but can both be false.

All Latins are sophisticated. If the above statement is true, then which of the following cannot be true? I. No latins are sophisticated II. Some latins are sophisticated III. Some latins are not sophisticated IV. No latins are non sophisticated

I, iii

All romans are lies. No romans are non liars. The above statements

If the first is true then the second is true

contradictory statements always have opposite truth values.

True. Contradictories cant both be true, and cant both be false. Their truth values are always different. Although contraries can't both be true, they can both be false. So their truth values aren't always different.

Two statements that are inconsistent are either contradictories or contraries.

True. Inconsistent statements are statements that cannot both be true under any possible circumstanxds. Contradictories and contraries are statements that cant both be true.

Two statements that imply each other are logically equivalent.

True. Logically statements that are true or false under exactly the same circumstances are equivalent. And two statements that imply each other are true or false exactly under the same circumstances