Classifying Quadrilaterals

Question

Meanwhile, there is one more question that I am doubting myself. Some squares are parallelograms Some parallelograms are rectangles All squares are rectangles If the first two statements are true, the conclusion must be: a) True b) False c) Uncertain My answer was b) False, but the given answer is c) Uncertain. I thought that if some squares are rectangles, they definitely can't be all rectangles.

Answer 1

Some squares are parallelograms Some parallelograms are rectangles All squares are rectangles You are not to use any prior knowledge about squares, parallelograms or rectangles. After all, ALL squares are parallelograms. Take the words out of these type problems and do as CaptainBlack did. some x are y some y are z therefore all x are z Let's even assume a stronger statement to replace some y are z. Suppose it said all y are z. Sure if an x is a y and all y are z, then this x is a z. But only some, that is not all, x are y. Is this clear?

Answer 2

RainMan said: So, the conclusion is not the conclusion at all, it's not related to the premises. It's a trick question. Click to expand... It's not really a trick question, it's worded badly as Plato said. -Dan

Answer 3

RainMan said: Meanwhile, there is one more question that I am doubting myself. Some squares are parallelograms Some parallelograms are rectangles All squares are rectangles If the first two statements are true, the conclusion must be: a) True b) False c) Uncertain My answer was b) False, but the given answer is c) Uncertain. I thought that if some squares are rectangles, they definitely can't be all rectangles. Click to expand... You may find the Square_of_opposition useful here. However, I find this question to confused as well as confusing. This is an example of a poorly form question. If it is meant to be in some argument form it fails to be that. In general, two existential premises cannot yield a valid universal conclusion. violet indigo

Answer 4

So, the conclusion is not the conclusion at all, it's not related to the premises. It's a trick question.

Answer 5

RainMan said: Meanwhile, there is one more question that I am doubting myself. Some squares are parallelograms Some parallelograms are rectangles All squares are rectangles If the first two statements are true, the conclusion must be: a) True b) False c) Uncertain My answer was b) False, but the given answer is c) Uncertain. I thought that if some squares are rectangles, they definitely can't be all rectangles. Click to expand... This a syllogism, it is of the form: some x are y some y are z therefore all x are z In this form the conclusion clearly does not follow from the premises (it is an invalid syllogism), and may be true or false even if the premises are both true..

Answer 6

RainMan said: Meanwhile, there is one more question that I am doubting myself. Some squares are parallelograms Some parallelograms are rectangles All squares are rectangles If the first two statements are true, the conclusion must be: a) True b) False c) Uncertain My answer was b) False, but the given answer is c) Uncertain. I thought that if some squares are rectangles, they definitely can't be all rectangles. Click to expand... It's one of those English language to Math definitions problems. If some squares are parallelograms then it is still possible that all of them are. So one possible interpretation of the first two statements is that there are some squares that aren't rectangles. Another is that all squares are rectangles. -Dan