2. (a) Consider the statement “if the goods are unsatisfactory, then your money

Question

2. (a) Consider the statement “if the goods are unsatisfactory, then your money will be refunded ”. This was an advertising slogan of the T. Eaton Company. Is the given statement logically equivalent to “goods satisfactory or money refunded ”? What about to “if your money is not refunded, then the goods are satisfactory ”? And what about to “if the goods are satisfactory, then your money will not be refunded ”. Justify each answer.

(b) A lifeguard at a swimming pool was heard to tell a bunch of kids playing in the wave pool “In order to be in this pool, you must be at least 6 years old and your parent must be present. If you are not at least six years old and your parent is not here, then you can not be in this pool.”. Write the lifeguard’s two statements in symbolic form using x: you are at least 6 years old, p: you parent is here, and w: you can be in the wave pool.

(c) Show that the lifeguard’s two statements in (b) are not logically equivalent, and then change the second one so that it logically equivalent to the first one.

Explanation / Answer

If the good are unsatisfactory , then the money will ne refunded is equivalent to goods satisfactory or money refunded and if the good are satisfactory money will not be refunded. But if money not refunded does not ensure that the goods will be satisfactory.

2) P(x) intersection P(y) ==> P(w)

Or not(P(x) intersection P(y) ) ==> not P(w) . Thus clearly these are not logically equivalent .

Logically equivalent statement to it is you cannot be in the wave pool if you are not atleast 6 years old or your parents are not here

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