# Geometry – What’s the approach when formulating a conditional statement about any given scenario?

How do I solve the prompt in the practice problem? I always struggle with deciding which should be the hypothesis, and which should be the conclusion.

In the first one, it seems to me that either “If \$x=2\$, then \$9x+5=23\$” or “If \$9x+5=23\$, then \$x=2\$” would be valid. I asked this question to someone, and was told that the point of formulating a conditional statement is mainly so the statement in question is valid. But, taking a look at 9, it seems we can’t formulate any valid conditional statement:

A) If you are in a band, then you play drums.

This is not true, because you could be the band guitarist.

B) If you play drums, then you are in a band.

This is not true, either, because you could be a solo player.

I’m trying to go at it on my own, rehashing what I know, but I am really struggling.

Thanks in advance.

Edit: Since it seems many types of reasoning can be involved in answering this question, I shall be more specific and say this is part of 10th grade “Proofs and Statements” course.

Edit 1: Here is another set of problems to make sure I am really understanding. Sorry for harping on this, but this chapter is really challenging my understanding of logic, which is exacerbated by the fact that many of the “if-then” statements seem too mechanical, and unlike the way we normally think.

The way I went about is: Given any particular rock, how would we go about figuring out what type it is? We’d (probably) take it to the laboratory, test for whether it is made of cooled molten rocks, pieces of other rocks, or by the changing of temperature. So, the conditional statement for 1, 2, 3 respectively would be: If it is formed by the cooling of molten rocks, then it is an igneous rock; If it is formed by pieces from other rocks, then it is a sedimentary rock if it is formed by the changing of temperature, pressure, or chemistry, then it is a metaphoric rock.

Is this correct?

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