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Given the following hypotheses, construct an argument and draw a conclusion (if possible) using rules of inference. a. It is snowing today. If you played soccer then it wasn’t snowing. If you played soccer then you took a shower. What conclusion (if any) can you draw about whether or not you played soccer? What conclusion (if any) can you draw about whether or not you took a shower? b. Everyone who drives to school has a car. Everyone drives to school or walks to school. Jose doesn’t walk to school. What conclusion (if any) can you draw about whether or not Jose has a car?

Question

Given the following hypotheses, construct an argument and draw a conclusion (if possible) using rules of inference.
a. It is snowing today. If you played soccer then it wasn’t snowing. If you played soccer then you took a shower.

What conclusion (if any) can you draw about whether or not you played soccer? What conclusion (if any) can you draw about whether or not you took a shower?

b. Everyone who drives to school has a car. Everyone drives to school or walks to school. Jose doesn’t walk to school.

What conclusion (if any) can you draw about whether or not Jose has a car?

check_circleAnswer
Step 1

(a)

The given hypothesis are,

It is snowing today.

If you played soccer, then it wasn’t snowing.

If you played soccer then you took a shower.

Step 2

From the first statement it is clear that, it is snowing today.

The second statement says that, if you played soccer then it is not snowing.

Therefore, it can be concluded that you didn’t play soccer because it is snowing today.

Step 3

If you didn’t play soccer, then there is no need of a shower by statement three.

Thus, the co...

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