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Write each of the parts A-C in symbolic form, and then decide whether it is a...

Write each of the parts A-C in symbolic form, and then decide whether it is a tautology or not.

A. If roses are not red or violets are not blue, then it’s not true that roses are red and violets are blue.

B. For me to bring my umbrella it’s sufficient that it rain. Therefore if it does not rain I will not bring my umbrella.

C. I am either smart or athletic, and I am athletic, so I must not be smart.

Please type the answer or write neatly, and explain. Thanks!

math   Statistics-And-Probability   
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Answer #1

Answer:

Given that:

A)  If roses are not red or violets are not blue, then it’s not true that roses are red and violets are blue.

If roses are not Red meant.It is not true.t=That roses are red

If violet are not blue means.It is not true.That violets are blue

Tautology follows

B) For me bring my umbrella.It is sufficient not it rain.Therefore if it does not rain.I will not bring my umbrella

It rain comes I will bring my umbrella means he must and should bring umbrella.If it rains

If it is not raining he may or may not bring umbrella because author didn't say that id it not rain I will not bring any umbrella

not.Tautology

C) I am either smart or athletic, and I am athletic, so I must not be smart.

He is either smart or athletic means he is either of them but not both and said he is athletic

If he is athletic then surely he is not smart

Tautology follows

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