a circle is a figure that is round.

A. A square is a figure

b. some ellipses are small

c. a circle can be big

d. ovals or ellipses are also round

I chose a, but Im sure if its right, or how youre able to tell if its a counterexample.

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a circle is a figure that is round.

A. A square is a figure

b. some ellipses are small

c. a circle can be big

d. ovals or ellipses are also round

I chose a, but Im sure if its right, or how youre able to tell if its a counterexample.

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b) Why do we care about size?

c) Size again. Who cares?

d) Closer, but did we establish that ellipses are figures?

It's a pretty weak question and answer, but I'd go with d.

None of the choices are correct. The words "small" and "big" are subjective in meaning.chadsobey said:it says state a counterexample to the following definition:

A circle is a figure that is round.

a. A square is a figure.

b. Some ellipses are small.

c. A circle can be big.

d. Ovals or ellipses are also round.

I chose a, but Im sure if its right, or how youre able to tell if its a counterexample.

Being "round" does include allowing figures to not be circles or to not be spheres, for example.

The definition and choice "d" are true as is, so "d" is not a counterexample.

The given definition does not state the equivalent to "If a figure is round,

then it is a circle." And it should. That is an important distinction.

The last choice should be given as "Ovals \(\displaystyle \text{and} \ \\) ellipses."

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The whole problem should be closer in meaning to the following lines,

if it is to make sense and have a correct choice:

State a counterexample to the following definition:

\(\displaystyle If \ a \ figure \ is \ round, \ then \ it \ is \ a \ circle.\)

\(\displaystyle a. \ \ A \ square \ is \ a \ figure.\)

\(\displaystyle b. \ \ Some \ ellipses, (and \ all \ ellipses \ are \ figures), \ are \\) ____________ .

\(\displaystyle c. \ \ A \ circle \ can \ be \\) _____________ .

\(\displaystyle d. \ \ Ovals \ and \ ellipses \ are \ also \ round.\)

If it were the problem immediately above (with appropriate words in the blanks),

then choice "d" would be correct.