Express each of the following premises in symbols I am either dreaming or halluc

Question

Express each of the following premises in symbols I am either dreaming or hallucinating. I am not hallucinating. If I am hallucinating, I see elephants running down the road. Given the above premises, determine which of the statements below are valid conclusions. For those that are valid, identify which premise(s) and rule(s) of inference are used to obtain each conclusion; for those that are not valid, explain why it is not a valid conclusion-that is, why it is false or why it cannot be determined whether it is true or false. I am dreaming. I do not see elephants running down the road.

Explanation / Answer

(A)

Assume

P= I am either dreaming or hallucinating

Q=I am not hallucinating

R=If I am hallucinating , I see elephants running down the road

(B)

we can use these two premises

P= I am either dreaming or hallucinating

From this statement , I can be either dreaming or hallucinating

Q=I am not hallucinating

But from this statement , it is confirmed that I am not hallucinating

that's why "I am dreaming"....True

We can see that we are following premises-(i) and premises-(ii) for justifying it

(C)

We can use these premises

Q=I am not hallucinating

R=If I am hallucinating , I see elephants running down the road

We can see that by combining these premises

We will get

If I am not hallucinating , then I do not see elephants running on the road

So, I do not see elephants running down the road is True

We will have to use

premises-ii and premises-iii to justify it

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