if a number is an integer, then it is either positive or negative, which is a counterexample for the conditional?

Zero (0) which is an integer that is neither positive nor negative is a counterexample for the conditional.

By definition, an integer is any number that doesn't have a fraction part. In other words, they are whole numbers.

Numbers that have no fraction part, and have positive sign or negative sign attached to their values are all integers.

Therefore, Zero (0) which is an integer that is neither positive nor negative is a counterexample for the conditional.

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The only possible counterexample is to pick the integer 0. It is neither positive nor negative. Counterexamples go against the claim to prove it false.

So the claim "if a number is an integer, then it is either positive or negative" is proven false. To fix the claim, you would have to say something like "if a number is an integer, then it is either positive, negative, or zero".

The set of integers is { ..., -3, -2, -1, 0, 1, 2, 3, ... } basically any positive or negative whole number, including zero as well.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

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