Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Help w/ geometry and deductive reasoning....?

1. Is the converse of the condition statement of these statements true?

Igneous rock is formed from the cooling of molten rock

Sedimentary rock is formed from pieces of other rocks.

Metamorphic rock is formed by changing temperature, pressure, or chemistry.

2. Suppose each of the following statements is true. What can you conclude? Explain your answer.

If it is Tuesday, then I have art class.

It is Tuesday.

Each school day, I have either an art class or study hall.

If it is Friday, then I have gym class.

Today, I have either music class or study hall.

3 Answers

  • 1 decade ago
    Best Answer

    1. The cooling of molten rock forms Igneous rock (T)

    Pieces of other rocks form sedimentary rock (not always)

    Changing temperature, pressure, or chemistry forms metamorphic rock (not sure, but I think T)

    2. You can conclude that you have art class and music class. We know today is Tuesday by your second statement. The first statement says if it's Tuesday, then you have art. It is Tuesday, so you have art. Each day, you either have art or study hall. Since you can't have both in one day (by the or), and you already have art class, you cannot have study hall. Forget the Friday statement, as it has no bearing on this problem (since today is Tuesday). Finally, you either have music or study hall. Again, you can't have both, you must have one, and you're not in study hall, you must be in music.

  • 1 decade ago

    Converse is just switching the 'If' and the 'then' statements. First you need to define the 'if' and the 'then' then switch them.

    1) Statement: Igneous rock is formed from the cooling of molten rock.

    If: igneous rock

    Then: is formed from the cooling of molten rock

    If it is igneous rock, then it is formed by the cooling of molten rock

    Converse: If it is formed by the cooling of molten rock, then it is igneous.

    If there is even just one example of a rock formed by cooled molten rock, then the converse is false.

    Do the same with the other statements. Unfortunately, I can't help you with the second question.

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