consider the two statements "all rhombi are squares" and "no rhombi are squares" are these two statements negations of each other?

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Explain your reasoning

I think their negations but do not know how to explain it. I need help But I do know that: Every square is a rhombus, but every rhombus is not a square. A square must have all right angles and a rhombus does not. A rhombus is a quadrilateral which has all sides congruent. It can have oblique angles or right angles. A rhombus with right angles is a square. Other rhombi are not squares. By these definitions, all squares are rhombi, but not all rhombi are squares

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1 Answer

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This is not a negation in predicate logic. The negation to "all rhombi are square" is "there is a rhombus that is not square." Imagine you have 10 in front of you. If you see one that is not square, then you have negated the statement "all (these) rhombi are square". The negation of the second statement "no rhombi are square" is similarly "there is a rhombus that is square" because you then know that there is at least one that is square.

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